Simple Harmonic Motion

Question 1

What is simple harmonic motion?

Answer 1

It is defined as oscillating motion in which the acceleration is directly proportional to the displacement. Acceleration is in the opposite direction to displacement.

Question 2

Describe the motion of an object as it is released from a point on the side of its equilibrium position?

Answer 2

The object will accelerate towards the midpoint and then will decelerate to the maximum in the negative direction.Then it will accelerate back to the midpoint.

Question 3

What causes the object to accelerate towards the midpoint?

Answer 3

There is always a restoring force that attracts the object towards the midpoint and as a result the acceleration is in this direction.

Question 4

When is velocity,displacement and acceleration max?

Answer 4

Velocity is greatest when gradient of displacement graph is greatest.This is when displacement is zero and the object passes through equilibrium.Acceleration is max when gradient of velocity time graph is greatest.This is when velocity is zero and occurs at max displacement in opposite direction.Acceleration is zero when velocity gradient is 0 and velocity is max.

Question 5

What provides the restoring force for pendulums and horizontal springs?

Answer 5

GPE and EPE

Question 6

What is the sum of the potential and kinetic energy called and does it ever change?

Answer 6

It is called the mechanical energy and no it does not change unless the motion is damped.

Question 7

What is the angular frequency of an oscillation?

Answer 7

It is the angle turned per second and is equal to 2pif.

Question 8

What is the relationship between amplitude,frequency and time period?

Answer 8

Amplitude is always constant for a given oscillation and not related to the other two.Frequency and time period are unrelated to amplitude.

Question 9

What is the defining equation of simple harmonic motion?

Answer 9

a=-omega^2X

Question 10

What is the equation for max acceleration?

Answer 10

amax=omega^2xmax displacement

Question 11

What is the formula for max speed?

Answer 11

vmax=omegaxmax displacement.

Question 12

What is the graph for displacement?

Answer 12

x=max displacement*cos(wt)

Question 13

What are the two ways that you can alter the frequency of the SHM of a spring?

Answer 13

You can add extra masses as this makes the trolley heavier meaning the time for each oscillation will increase.Use weaker springs,these springs will have a lower restoring force hence oscillations will take longer.

Question 14

What is the formula for the restoring force of a spring?

Answer 14

F=-kx

Question 15

What is the formula for the time period of a spring?

Answer 15

T=2pi rootm/k k is spring constant

Question 16

What are free oscillations?

Answer 16

They occur when an object undergoes shm with the absence of friction so the amplitude of oscillations remain constant.

Question 17

What is the velocity formula for shm?

Answer 17

v=w+-root(A^2-x^2)

Question 18

What is damped motion?

Answer 18

This is where there are dissipative forces present that gradually reduce the amplitude of shm.

Question 19

What is light damping?

Answer 19

This is when the time period of an oscillation is independent of amplitude.But the amplitude of oscillations gradually decreases with time.The time period of the cycles is the same.

Question 20

What is critical damping?

Answer 20

This is when an object returns to equilibrium after being displaced in the shortest period of time.This stops any oscillations from occurring.

Question 21

What is heavy damping/over damping?

Answer 21

This is when an object is heavily damped that it takes longer than critical damping to reach the equilibrium position.There is virtually no oscillation and it returns to equilibrium very slowly.

Question 22

What is a periodic force?

Answer 22

It is an external force which is applied at regular intervals.

Question 23

What happens when a system oscillates without a periodic force being applied to it?

Answer 23

The system will be oscillating at its natural frequency.

Question 24

What type of vibrations does a system go under when a periodic force is applied to it?

Answer 24

The system goes under forced vibrations.

Question 25

What happens when you alter the driving frequency of an osicllator?

Answer 25

If the driving frequency is much less than the resonant frequency the oscillator and driver are in phase.However,if the driving frequency is greater than the resonant frequency the two will be in antiphase.

Question 26

What is resonance ?

Answer 26

Resonance occurs when the driving frequency=natural frequency.Here at this resonant frequency the oscillator has maximum amplitude.At resonance the phase difference is 90 degrees between the driver and oscillator.

Question 27

What is the phase difference between the displacement, velocity and acceleration time graphs.

Answer 27

Displacement and velcity 90 degrees out of phase.Velocity and acceleration 90 degrees out of phase.

Question 28

What is a full cycle of SHM?

Answer 28

It is a full cycle starting from the ticker is released from max positive displacement at the right.

Question 29

Describe the pendulum SHM experiment.

Answer 29

Connect a pendulum to an angle sensor which is connected to a computer.This will plot a displacement time graph and you can determine the period of oscillation from it.Otherwise use a fiducial marker to indicate a reference point.Using a stopwatch measure time taken n numbers of oscillations and divide by n.See how T^2 varies with 1/k,m and T varies with amplitude.

Question 30

Describe the mass spring SHM experiment.

Answer 30

Connect a trolley of mass m to a horizontal spring.You can get a computer to plot a displacement time graph using a data logger connected to a position sensor.Alternatively you could use a stopwatch but this may cause a random error.See how T varies with m and A and how T^2 varies with l.

Question 31

How does damping affect resonance?

Answer 31

Light damping causes a larger and sharper resonance peak.The resonant frequency is closer to the natural frequency.For heavy damping resonance occurs at a driving frequency slightly lower than the natural fequency.