1. The displacement x cm of a particle moving in a straight line is given by this equation.
x = 6cos(3t + π/6)
Find:
a. the amplitude
b. the initial velocity of the particle
c. the initial position of the particle
d. the frequency of the particle
e. the time to first reach the centre of the motion
2. A particle is performing simple harmonic motion and starts from rest at a point 4 metres to the right of the centre of motion. It travels for 10 seconds before again being instantaneously at rest.
a. Find the equation of motion in the form
x = a cos (nt + α)
b. Find the maximum speed reached.
c. Find how long it has been moving when it first reaches a point halfway from the starting point to the centre. Find its speed and acceleration at this point.
3. A particle is performing simple harmonic motion with a period of 6π seconds. After 5 seconds it is 10 metres from the centre travelling at 5 m/s.
Calculate:
a. The amplitude
b. The initial phase
c. The maximum speed
