Question

A particle moving along the x – axis in simple harmonic motion starts from the equilibrium position, the origin, at time t = 0 and moves to the right. The position of the particle after time, t, is given by the following equation: 𝑥 = 2.0 sin 3𝜋𝑡 m Calculate:

i. The maximum velocity of the motion.

ii. The acceleration of the object after 2 seconds (i.e. at t = 2 s).

iii. The distance travelled by the particle from t = 0 s to t = 2 s.

Answer 1

Maximum velocity:

$$v_\text{max}=2·3\pi=6\pi\text{ m/s}.$$

The acceleration:

$$a=x"(t)=-18\pi^2\sin(3\pi t)=-57\text{ m/s}^2.$$

The distance:

$$d=\int^2_0x'(t)\text dt=0.$$