Question

An object moves in simple harmonic motion with period 6 seconds and amplitude 7cm. At time t=0 seconds, its displacement d from rest is -7cm, and initially it moves in a positive direction.

Give the equation modeling the displacement d as a function of time t.

Answer 1

The equation modeling the displacement 'd' as a function of time  is d (t) = 7 sin ( 3π t)

What is simple harmonic motion?

Simple harmonic motion can be defined as a periodic motion of a point in a straight line, such that its acceleration is towards a fixed point and is proportional to its distance from that point to the line.

It is derived from the projection to the axis of a circle of a point in constant speed on the circumference

Displacement is represented thus;

d ( t ) = A sin⁡ ( 2 π f t )

T = 1/f

Where,

• d is the displacement
• A is the amplitude = 7cm
• T is the period = 6 seconds

Note that there is no phase shift

d (t) = 7 sin ( 2π × 1/ 6 t)

d (t) = 7 sin ( 2π/6 t)

d (t) = 7 sin ( 3π t)

Thus, the equation modeling the displacement 'd' as a function of time  is d (t) = 7 sin ( 3π t)

Learn more about simple harmonic motion here:

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