Question

A spring with spring constant 13.1 N/m hangs from the ceiling. A ball is suspended from the spring and allowed to come to rest. It is then pulled down 10.0 cm and released. The ball makes 22.0 oscillations in 20.0 seconds.

What are its (a) mass and (b) maximum speed?

Answer 1

Step-by-step explanation:

spring constant, K = 13.1 N/m

22 oscillations in 20 seconds

time taken to complete one oscillation is called time period.

T = 20 / 22 second = 0.909 seconds

(a) let m be the mass.

The formula for the time period is

`T = 2\pi \sqrt{(m)/(K)}`

`m = (T^(2)K)/(4\pi ^(2))`

`m = (0.909^(2)* 13.1)/(4\pi ^(2))`

m = 0.275 kg

(b) maximum speed, v = ω A = 2π A / T

v = ( 2 x 31.4 x 0.1) / 0.909

v = 0.691 m/s