Question

If the distance d of an object from its rest

position at time t is given by a sinusoidal graph, the motion of the object is simple harmonic motion.

Short answer

The given statement is true

Step-by-step solution

Given information

If the distance d of an object from its rest

position at time t is given by a sinusoidal graph, the motion of the object is simple harmonic motion.

Explanation for true statement

The simple harmonic motion can be modeled as $$\begin{gathered} d=a\sin \left(\omega t\right) \\ d=acos\left(\omega t\right) \end{gathered}$$

This means that the motion of the object whose displacement d from its rest position at time t is modeled by a sinusoidal graph is simple harmonic

Hence the statement is true

Conclusion

The given statement is true statement