simple harmonic motion Flashcards
What are the two conditions required for an object to be in simple harmonic motion?
- The acceleration is proportional to the displacement
- The acceleration is in the opposite direction to the displacement
What are examples of objects that undergo SHM AND how are they periodic?
- The pendulum of a clock
- A mass on a spring
- Guitar strings
- The electrons in alternating current flowing through a wire
These are always periodic, meaning they are repeated in regular intervals according to their frequency or time period
What is a restoring force and its significance in SHM?
- An object in SHM will also have a restoring force to return it to its equilibrium position
- This restoring force will be directly proportional, but in the opposite direction, to the displacement of the object from the equilibrium position
- the restoring force and acceleration act in the same direction
Why is a person jumping on a trampoline not an example of SHM?
- The restoring force on the person is not proportional to their distance from the equilibrium position
- When the person is not in contact with the trampoline, the restoring force is equal to their weight, which is constant
- This does not change, even if they jump higher
What do the components of SHM acceleration equation mean?
What does the SHM acceleration equation demonstrate?
- The acceleration reaches its maximum value when the displacement is at a maximum ie. x = A (amplitude)
- The minus sign shows that when the object is displaced to the right, the direction of the acceleration is to the left and vice versa (a and x are always in opposite directions to each other)
Relationship between SHM acceleration and displacement
directly proportional
What are the features of a displacement-acceleration graphfor an object in SHM
What are the components of the SHM displacement equation
When is displacement at max, according to the SHM displacement equation
- The displacement will be at its maximum when cos(⍵t) equals 1 or −1, when x = A
What is the equation used when an object is oscillating from its equilibrium position (x = 0 at t = 0)
(The displacement will be at its maximum when sin(⍵t) equals 1 or −1, when x = A.
This is because the sine graph starts at 0, whereas the cosine graph starts at a maximum)
when is the greatest speed of an oscillator
when it is in the equilibrium position
What do the components of the SHM speed equation mean
What does the SHM speed equation show
That when an oscillator has a greater amplitude A, it has to travel a greater distance in the same time and hence has greater speed v
Are the displacement, velocity and acceleration graphs for an object in SHM in phase_
No- the displacement, velocity and acceleration graphs in SHM are all 90° out of phase with each other
What are the key features of a displacement-time graph for an object in SHM
- The amplitude of oscillations A can be found from the maximum value of x
- The time period of oscillations T can be found from reading the time taken for one full cycle
- The graph might not always start at 0
- If the oscillations starts at the positive or negative amplitude, the displacement will be at its maximum
What are the key features of a velocity-time graph for an object in SHM
- It is 90 degrees out of phase with the displacement-time graph
- Velocity is equal to the rate of change of displacement
So, the velocity of an oscillator at any time can be determined from the gradient of the displacement-time graph
What are the key features of an acceleration-time graph for an object in SHM
- The acceleration graph is a reflection of the displacement graph on the x axis
- This means when a mass has positive displacement (to the right) the acceleration is in the opposite direction (to the left) and vice versa
- It is 90° out of phase with the velocity-time graph
- Acceleration is equal to the rate of change of velocity
So, the acceleration of an oscillator at any time can be determined from the gradient of the velocity-time graph:
Equation to find v from x and t for SHM
Equation of find a from v and t for SHM
What do the components of the maximum speed equation for SHM mean
When is the maximum speed for a mass on a spring
at the equilibrium position. Its speed is 0 at its positive and negative amplitude
What do the components of the maximum acceleration equation for SHM mean
Why does an object in SHM still have acceleration at maximum amplitude
- Although at the amplitude, the speed is zero, the oscillator has changed direction
- This means that it has a non–zero velocity, and since acceleration is the rate of change of velocity, the oscillator has an acceleration at the amplitude too
At what point does an object in SHM have maximum acceleration
at its positive and negative amplitude. Its acceleration is 0 at the equilibrium position
What do the components of the time period for a mass-spring system equation mean