A spring with spring constant 15.5 N/m hangs from the ceiling. A ball is suspended from the spring and allowed to come to rest. It is then pulled down 7.00 cm and released. The ball makes 37.0 oscillations in 22.0 seconds. 1) What is its the mass of the ball? 2) What is its maximum speed?

A) 138.8g

B) 73.97 cm/s

Explanation:

K = 15.5 Kn/m

A = 7 cm

N = 37 oscillations

tn = 20 seconds

A) In harmonic motion, we know that;

ω² = k/m and m = k/ω²

Also, angular frequency (ω) = 2π/T

Now, T is the time it takes to complete one oscillation.

So from the question, we can calculate T as;

T = 22/37.

Thus;

ω = 2π / (22/37) = 10.5672

So, mass of ball (m) = k/ω² = 15.5/10.5672² = 0.1388kg or 138.8g

B) In simple harmonic motion, velocity is given as;

v (t) = vmax Sin (ωt + Φ)

It is from the derivative of;

v (t) = - Aω Sin (ωt + Φ)

So comparing the two equations of v (t), we can see that;

vmax = Aω

Vmax = 7 x 10.5672 = 73.97 cm/s