What is the maximum displacement from its resting position?

Question

The displacement d (in meters) of an object at time t (in seconds) is given.
(a) Describe the motion of the object.
(b) What is the maximum displacement from its resting position?
(c) What is the time required for one oscillation?
(d) What is the frequency?

d = 6 + 2 cos (2πt)

Answer 1

Step 1:

a)

The displacement of the object is

The above equation is in the form of simple harmonic motion

Where is a displacement in time t , is the amplitude and period is .

Compare above two equations ,

.

The motion of the object is simple harmonic motion.

b)

The maximum displacement of the object from its resting position is the amplitude.

meters.

The amplitude is meters.

Step 2:

(c)

The time required for one oscillation is the period.

The period is .

d)

Frequency is the reciprocal of the period.

.

The frequency is oscillations per second.

Solution :

a) The motion of the object is simple harmonic motion.

b) The amplitude is meters.

c) The period is .

d) The frequency is oscillations per second.