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Level 107

### Circular Motion & Simple Harmonic Motion

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Resonance
a phenomenon that occurs when two objects naturally vibrate at the same frequency; the sound produced by one object causes the other object to vibrate
It needs a vertical component of the tension to balance the weight of its vertical mass.
Why is it impossible for the string to be horizontal as the mass rotates in a horizontal plane?
Explain the meaning of the term damping
A resistive force that acts on the oscillating system that causes energy to be dissapated.
Why must there be a centripetal force acting towards the centre of the circle?
To keep a mass moving in a circle it requires a centripetal force acting towards the centre.
Define angular velocity.
The rate of change of angular displacement.
Describe the function of a centripetal force.
Allows motion of a body to go in a circular path.
Towards the centre of a circle.
State the direction of the centripetal force.
At the extremities.
State where the maximum acceleration occurs in the motion of a pistion.
Define simple harmonic motion.
The acceleration of a body is directly proportional to the displacement from a fixed point and it always acts towards that point.,
Give an example of a system involving forced vibrations which have a characteristic response.
Tuning a radio or television to a particular station is an example of electrical resonance.
State how the force acting on the particle depends on its displacement from the equilibrium position.
The force acting on the particle is directly proportional to the displacement from the fixed point and the force always acts towards that fixed point.
Define linear velocity.
The rate of change of linear displacement.
It is a vector because velocity has a direction.
Linear velocity is a vector quantity, because it has both a magnitude and a direction. Suggest whether angular velocity is also a vector.
Define amplitude
The maximum displacement from the fixed point
Define period
Time taken to complete one oscillation.
Amplitude decreases with time.
How could you tell a pendulum is lightly damped?
What is the cause of the damping?
A resistive force that acts on the oscillating system such as air resistance.
rads-1
State the SI unit of angular velocity
the Amplitude
What does A in the shm equation represent?
State concisely how a mechanical system, capable of oscillation, may be made to resonate.
When the driving frequency of the fore vibrator is equal to its natural frequency of the system and therefore it vibrates with a large amplitude.
acceleration is directly proportional to the displacement
State how the magnitude of the acceleration of the particle depends on its displacement from the fixed point.
the acceleration alway acts towards the fixed point
Describe the variation of the direction of the acceleration of the particle.
equation linking amplitude and displacement
x = A cos (omega t)
F = -kx
equation for SHM (simple harmonic motion)
omega = 2 pi / T
equations for angular frequency--not squared (omega)
x = A cos (omega t)
equation for displacement, in the context of SHM
v = -A omega sin (omega t)
equation for velocity, in the context of SHM
equations for acceleration, in the context of SHM
a = -A omega2 cos (omega t) = -omega2 x
a
acceleration (m/s2)
equation linking angular frequency and acceleration
a = -A omega2 cos (omega t)
equation linking acceleration and amplitude
a = -A omega2 cos (omega t)
1
what is the maximum possible value of sin (omega t) or cos (omega t) [in SHM]
A omega
symbols equal to maximum velocity (SHM)
A omega2
symbols equal to maximum acceleration (SHM)
a = -omega2 x
equation linking displacement and acceleration
omega2 = k / m
equation linking the squared angular frequency and mass