An object undergoing simple harmonic motion takes 0.34 s to travel from one point of zero velocity to the next such point. The distance between those points is 27 cm. Calculate (a) the period, (b) the frequency, and (c) the amplitude of the motion.

a) T = 0.68 s,  b)  f = 1.47 Hz, c) λ = 54 m

Explanation:

Simple harmonic motion is described by the expression

         x = A cos (wt + Ф)

a) angular velocity and period are related

         w = 2π / T

The period is the time it takes for the movement to repeat itself, in this case they indicate the time to reach two consecutive zeros, this corresponds to half a period

            T / 2 = 0.34 s

            T = 2 0.34

            T = 0.68 s

b) period and frequency are inverse

             f = 1 / T

             f = 1 / 0.68

             f = 1.47 Hz

c) the amplitude of the movement is proportional to the energy carried by the wave, which cannot be calculated with the data provided.

With the length data we can find the wavelength

            λ / 2 = 27 m

            λ = 54 m

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