Question

An object moves in simple harmonic motion with period 8 seconds and amplitude 6 cm. At time t = 0 seconds, its displacement d from rest is -6 cm,
and initially it moves in a positive direction.
Give the equation modeling the displacement d as a function of time t.
d = 0
昌 石
UT
CD

Answer 1

In the equation model, the simple harmonic motion is d=6sin(πt/4)-6 if the object moves in simple harmonic motion with a period of 8 seconds and amplitude of 6 cm.

What is simple harmonic motion?

Simple Harmonic Motion is described as a motion in which the restoring force is proportionate to the body's displacement from its mean position.

We have:

Amplitude A = 6 cm

Time period = 8 seconds

T = 2π/w

8 = 2π/w

w = π/4

Its displacement d from rest is -6 cm, and initially, it moves in a positive direction.

d(0) = -6 cm at t = 0

The equation becomes:

$\rm d = 6sin(\dfrac{\pi}{4}t)-6$

Thus, in the equation model, the simple harmonic motion is d=6sin(πt/4)-6 if the object moves in simple harmonic motion with a period of 8 seconds and amplitude of 6 cm.

Learn more about the simple harmonic motion here:

brainly.com/question/17315536

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