Asmall block is attached to an ideal spring and is moving in shm on a horizontal, frictionless surface. the amplitude of the motion is 0.200 mm and the period is 3.28 ss .

part a
what is the acceleration of the block when x= 0.160m ?
express your answer with the appropriate units.

part b
what is the speed of the block when x= 0.160m ?
express your answer with the appropriate units

a = -0.59 m/s^2

v = 0.22 m/s

Explanation:

The equation of motion in simple harmonic motion is defined as

where A is the amplitude, ω is the angular frequency, and Ф is the phase angle which has to be determined by initial conditions.

The period of the motion is given, so the angular frequency could be calculated.

The initial conditions are not given in the question, so I will assume that at t = 0, the block is at the origin (x = 0). (This assumption will not affect our final result, we can as well choose another initial point.)

Let’s find the time when x = 0.160 m.

The velocity function is the derivative of the position function with respect to time.

Similarly, the acceleration function is the derivative of velocity function with respect to time.

A)

B)

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