Unit 4: Simple harmonic motion Flashcards
Describe one full cycle of motion
From maximum height at one side to maximum height on the other side and then back again
What is the lowest point of a swing referred to as?
The equilibrium position as this is where it will come to a standstill
Describe the motion of an oscillating object
An oscillating object moves repeatedly one way then in the opposite direction through its equilibrium position
What is displacement in terms of the equilibrium position?
The distance and direction from the equilibrium position
What is the amplitude of oscillations?
The maximum displacement of the oscillating object from equilibrium
What are features of free oscillations?
The amplitude is constant and there are no frictional forces
What is the time period?
The time for one complete cycle of oscillations
What is frequency and what is its unit?
The number of cycles per second and its unit is the hertz
What is the formula that relates time period and frequency?
T = 1/f
What is the formula for angular velocity in terms of the time period?
ω = 2π/T
What is the unit of angular velocity?
Radians per second
How can you tell if two objects are oscillating out of phase?
One object will reach maximum displacement on one side at a certain time, Δt, later than the other object
What is the formula for the phase difference in radians when two objects are oscillating at the same frequency and how is it different if you want the phase difference in degrees?
2πΔt/T in radians and 360Δt/T in degrees where Δt is the time between successive instants when the two objects are at maximum displacement in the same direction
Does the phase difference of two objects oscillating stay the same?
Yes
When do two objects oscillate in phase?
If Δt = T
What is a phase difference of 2π equal to?
0
How does the velocity of an oscillating object change in terms of the equilibrium?
An oscillating object speeds up as it returns to equilibrium and it slows down as it moves away from equilibrium
When will the amplitude of the oscillations be constant?
Provided friction is negligible
What does the gradient of a displacement-time graph represent?
Velocity
What does the gradient of a velocity-time graph represent?
Acceleration
When is the velocity of an object greatest?
When the gradient of the displacement-time graph is greatest i.e. when the object passes through equilibrium
When is the velocity zero?
When the gradient of the displacement-time graph is zero i.e. at maximum displacement
When is the acceleration greatest?
When the gradient of the velocity-time graph is greatest, this occurs when the velocity is zero and occurs at maximum displacement in the opposite direction
When is the acceleration zero?
When the gradient of the velocity-time graph is zero (the speed is at a maximum), this is when the displacement is zero
In which direction does acceleration act in terms of displacement?
The acceleration is always in the opposite direction to the displacement
What is simple harmonic motion defined as?
Oscillating motion in which the acceleration is proportional to the displacement and always in the opposite direction to the displacement
What does the constant of proportionality depend on in the simple harmonic equation and what produces a greater constant?
The time period of the oscillations and the constant is greater the shorter the time period as this means faster oscillations and therefore larger acceleration at any given displacement
What is the formula for simple harmonic motion?
a = -(ω^2)x where ω = 2π/T
What is the time period independent of?
The amplitude of the oscillations
What does the variation of displacement with time depend on ?
The initial displacement and the initial velocity
What is the SHM equation for the displacement when x = +A when t = 0 and the object has zero velocity at that instant?
x = Acos(2πft) where 2πft is in radians
What are SHM curves described as?
Sinusoidal
What is the general solution of a = -((2πf)^2)x?
x = Asin((2πft)+Φ) where Φ is the phase difference between the instants t = 0 and when x = 0
For any oscillating object, in which direction does the resultant force act?
The resultant force acting on the object acts towards the equilibrium position
What is the resultant force in SHM described as and why?
The restoring force as it always acts towards equilibrium
When is the acceleration (acting towards the equilibrium) proportional to the displacement
Provided the restoring force is proportional to the displacement from equilibrium
How can you test the oscillations of a mass-spring system?
Use two stretched springs and a trolley, when the trolley is displaced then released, it oscillates backwards and forwards, the first half-cycle of the trolley’s motion can be recorded using a length of ticker tape attached at one end to the trolley, when the trolley is released, the tape is pulled through a ticker timer that prints dots on the tape at a rate of 50 dots per second
What is done with the tape from the experiment of a mass-spring system?
A graph of displacement against time for the first half cycle can be drawn using the tape, the graph can be used to measure the time period which can be checked if the trolley mass m and the combined spring constant k are known
What can be used to record the oscillating motion of the trolley in the oscillating mass-spring system experiment?
A motion sensor linked to a computer
Why is the frequency of an oscillating spring reduced when the mass is increased?
The extra mass increases the inertia of the system, at a given displacement the object would therefore be slower than if the extra mass had not been added, each cycle of oscillation would therefore take longer
Why is the frequency of an oscillating spring reduced if weaker springs are used?
The restoring force on the trolley at any given displacement would be less so the object’s acceleration and speed at any given displacement would be less so each cycle of oscillation would therefore take longer
What is the formula for the time period of a mass spring system?
T = 2π(m/k)^1/2