Question

A simple harmonic oscillator's position is given by

y(t) = (0.860 m)cos(10.2t − 5.65).

Find the oscillator's position, velocity, and acceleration at each of the following times. (Include the sign of the value in your answer.)

(a)    

t = 0

position	m
velocity	m/s
acceleration	m/s2

(b)    

t = 0.500 s

position	m
velocity	m/s
acceleration	m/s2

(c)    

t = 2.00 s

position	m
velocity	m/s
acceleration	m/s2

Answer 1

The position of the oscillator is given by,

The velocity of the oscillator is given by,

The acceleration of the oscilllator is given by,

Now we will be just substituting the values (all the angles are taken as radians)

(a) t = 0,

Position is,

Velocity is,

Acceleration is,

(b) at t = 0.5 s

Position is,

Velocity is,

Acceleration is,

(c) at t = 2 s

Position is,

Velocity is,

Acceleration is,