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What is the maximum displacement from its resting position?

0 votes
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)
asked Jan 29, 2015 in PRECALCULUS by anonymous

1 Answer

0 votes

Step 1:

a)

The displacement of the object is

The above equation is in the form of simple harmonic motion image

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

Compare above two equations ,

image.

The motion of the object is simple harmonic motion.

b)

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

image meters.

The amplitude is image meters.

Step 2:

(c)

The time required for one oscillation is the period.

image

The period is image.

d)

Frequency is the reciprocal of the period.

image.

The frequency is image oscillations per second.

Solution :

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

b) The amplitude is image meters.

c) The period is image.

d) The frequency is image oscillations per second.

answered Jan 30, 2015 by james Pupil
edited Jan 30, 2015 by james

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