Simple Harmonic Motion Flashcards
State features of simple harmonic motion
The time period is independent of the amplitude
As the amplitude of the swing decreases the max velocity decreases, time is constant
Constant time period
Define period
The time taken for one complete oscilation
Define frequency
The number of complete oscillations per unit time
Describe the force and acceleration of simple harmonic motion
The oscillation has an equillibrium position and a force is required to displace the object from it
There is a restoring force which is always toward the equillibrium position hence the acceleration is also towards the equillibrium position
The greater the restoring force the greater the acceleration directed towards equilllibrium
The acceleration is directly proportional to the to the distance from the equilibrium position
Acceleration is in the opposite direction to displacement
What does isochronus mean
The period is independent of the amplitude
What is w^2 in the equation a=-w^2x
Angular frequency
Give an equation linking elasticPE and KE
1/2KA^2=1/2mv^2+1/2Kx^2
Give 2 equation for velocity using cos and sin
V=-Acoswt
V=-Asinwt
Give an eqaution for max velocity
V+2pifA
A= amplitude
Give an equation for angular frequency using spring constant
W^2=k/m
M=mass
When do you use sin ans cos for finding displacement
Use sin equation for when the object is begins at equilllibrium
Use cos when object begins at max or min displacement
Where do max EP energy and KE energy happen in SHM therfore describe the graphs
Energy is exchanges between kinetic and potential forms
MAs KE occurs at equillibrium position
Max EP occurs at amplitude position
Total E is conserved
EP is the inverse of KE graph where both graphs are a cos wave
Explain Damping
The process by which the amplitude of the oscillations decreases over time due to energy loss to resistive forces such as drag or friction
Give eg of light damping, heavy and critical damping
Light- pendulum swing in air
Heavy- pendulum swinging in water
Critical- pendulum oscillating in a thick syrup
How does the amplitude decrease in light damping
Exponentially
What happens in critical damping
The object stops before one complete oscillation
What is natural frequency
When an object oscillates without any external forces applied ( free oscillation)
What is forced oscillation
When a periodic driving force is applied to an object which cause the object to oscillate at a particular frequency
Resonance def
When the driving frequency is equal to the natural frequency of the object , when the amplitude of oscillation rapidly increases and will continue to until the system fails if there is no damping
When does maximum energy occur
When the driver is pi/2 radians ahead of the oscillator
When does resonance occur
When the frequency of the driver is very close to the natural frequency of the system , therfore the amplitude of the oscillator increases dramatically which can damage the oscillator
What can be done to reduce the resonance in a driven oscillator
You can use damping to reduce the height of the peak amplitude which increases the natural period therfore decrease in the natural frequency and therfore the resonance frequency
How do max KE and max elastic energy relate
Maximum KE = max Ee
How do you find maximum elastic potential energy
= (kA^2)/2
A= amplitude
Only for SHM
A mass is hung from the bottom end of a flexible string , explain how the mass can be made to reach resonance
Force the mass to oscillate with a periodic force, so that the mass will oscillate at max amplitude when the frequency of the driving force is equal to the natural frequency of the spring mass system
How can we find the spring constant of a spring using simple harmonic motion experiment?
Set up a clamp with a spring attached to a mass and a fiducial marker in line with the bottom of the mass Adam mass of 50 g to the spring and slightly stretched the spring so that the system oscillates statically wait until the bottom of the mass reaches the top of the fiducial marker then start a stop clock. This is the time the time taken for 10 oscillations where one oscillation is when the mass starts at the top of the marker goes down and returns back to the top of the marker This time by 10 to find the time period of the oscillations repeat for the same mass and find demean time period. Repeat this method for out to 500 g of mass in increments of 50 g then plot graph of T squared against mass so that the gradient is four pi squared divided by the spring constant, to improve accuracy we could carry out the experiments so that we could plot of force applied against extension and compare the values of spring constant
Equation= T^2=4pi^2m/k
How can we find the value of g using the pendulum experiment for simple harmonic motion?
Set up a clamp with a string and a bob attached wrap the top end of the string on a wooden block and clamp this wooden block so that there is a fixed pivot place a fiducial marker perpendicular to the string and aligned with the Bob measure the length of the string using a ruler then slightly swing the pendulum at about 10° angle and then time the time taken for 10 oscillations where one oscillation is when the Bob starts at the equilibrium position which is the facial marker goes to the left and then to the right and back to the equilibrium position this by 10 for the time period adjust the string and adjust the string length for a different length and repeat the experiment plot squared against L where the gradient is pi squared divided by G
Eqaution : T^2= 4pi^2/g
Student calculated the uncertainty of finding G using simple harmonic motion. They then calculated the percentage difference from their value. How can we determine using the percentages if the value found for G in the experiment is accurate
The value would be accurate if the percentage difference is smaller than the percentage uncertainty
A glider is placed in an air track with two springs attached either side. The glider is pulled so that it oscillate in simple harmonic motion horizontally when the initial displacement of the glider increases of the springs increases its extension while the extension of the other spring on the other side decreases explain why the maximum kinetic energy of the motion increases.
Initial displacement increases therefore amplitude increases however angular frequency remains constant
Therefore, elastic potential energy gained from stretching the spring is greater than the energy lost from the spring by compressing elastic potential energy is dependent on displacement squared therefore total energy increases so kinetic energy also increases as elastic potential energy is transferred to kinetic energy. This is when kinetic energy is maximum when X equals zero and at this point elastic potential energy is a minimum because it’s transferred to the kinetic energy.
How can engineers reduce the resonance of a structure such as a bridge?
Install shock absorber or dampers
And Stefan, the structure by using reinforcement
Sand is placed on top of a vibrating surface which remains at a constant frequency however above a particular frequency whilst vibrating the sand grains lose contact with the surface explain why and how
When the vibrating surface accelerates down with an acceleration less than the acceleration of freefall the sand full stay in contact with the surface as there is a contact force however above a particular frequency the acceleration downward will be greater than the value of G therefore there’s no longer any contact force on the sand so the sand do not stay
What is the phase difference between the particle velocity and the particle displacement in simple harmonic motion?
Pi over 2 rad
Describe the kinetic energy and potential energy graphs, of a simple harmonic motion system
The potential energy is a positive quadratic about t the origin and the kinetic energy is a negative quadratic. Both graphs are in the positive region of why
There is always two cycles before the time period for both of these graphs
How can we find the time period when we are given the mass of an object and the amplitude of the oscillations of an object in simple harmonic motion? We are given the total energy.
Total energy= kA^2\2
Therefore reform an equation with the total energy and the amplitude to find the spring constant K
Then use the equation T^2=4pi^2m/k to find the time period
Describe the shape of a graph of the velocity against displacement in a simple harmonic motion
It is a circle
What happens to acceleration as speed decreases in SHM
It incraeses
Give an example for useful resonance and an example where resonance is a problem, state driver and driven
Microwaves(driver) causing water molecules to resonate
Problem
Walkers(driver) causing bridge to resonate
State a difficulty with the pendulum experiment and provide a solution
The angle of swing reducing over time due to natural damping
Sol= video the motion with an onscreen timer and analyse
how is the damping force and velocity related
damping force is always in the opposite direction to velocity
a tower has a natural frequency of 0.15 hz in the strongest wind , inside the tower there is a bal spring system which oscillates in SHM this drives oil through small holes to provide damping. the vibrational wnergy of the sphere is converted to thermal energy. explain why the natural frequency of the ball system must also be 0.15 HZ
max energy is transferred between the driver(tower) and the sphere(driven) when the sphere is at the natural frequebncy of the tower therfore causing damping
a spherical mass is placed in between 2 springs (attached) why does the mass oscialte in SHM when placed horizontaly ( springs are parallel to floor)
there is a restoring force towards the equillibrium position opposite to dislacement, the resultant force from the springs is prportional to the displacement from the centre
a mass is hung from the bottom end of a flexible spring, how can the mass be made to show resonance
force the mass to ocsilate with a periodic force, therfore the mass will osscilate with max A when the frequency of the periodic force is the same as the natural frequency of the spring mass system
an ocsillator is damped in air a graph of displacement against time is ploted ( sin graph) at which time will the oscillatopr dissipate max energy
at t=0 as it has max velocity before being damped, therfore max KE dissipatyed as there is greatest friction
a vertical mass spring system is set up, it is now made to oscilate in air with SHM describe the energy changes as the mass moves from the lowest point in its motion through the equillibrium position to the highest point in its motion
KE starts at 0 and ends at ) at the amplitude ( lowest and highest point= A)
at equillibrium position KE will be max
the air will gain thermal energy as total E decreases over time
at lowest point min GPE max EPE , EPE decreases as it moves up GPE increases EPE is never 0
a pedulum is oscillating in air, a student notices that the A of each oscillation decreases overtime explain why and the effect it has on T
no effect on T T is independent of amplitude
there is a transfer of energy from the pendulum to the thermal energy store of the air due to air resistance
explain how velocity links with height in the pendulum experiment
KE=GPE
1/2 x m x v^2 = mgh
rearrange
