Question

A spring with spring constant 14 N/m hangs from the ceiling. A ball is attached to the spring and allowed to come to rest. It is then pulled down 7.0 cm and released. The ball makes 29 oscillations in 25 s seconds.

a) What is its the mass of the ball?

b) What is its maximum speed?

Answer 1

According to the given problem,

Given,

spring constant k = 14N/m

amplitude A = 7.0 cm = 0.07 m

frequency f = number of oscillations/time

                  = 29 / 25 s

                  = 1.16 Hz

angular speed ω = 2πf

                         = (2)(3.14)(1.16 Hz)

                         = 7.2885 rad/s

a)Using the angular spee relation of spring-mass system ,

ω = √(k/m)  

mass m = k/ω²   

m = (14 N/m) / (7.3 rad/s)²

m = 0.264 kg

b)Maximum velocity v_max = Aω

                                    = (0.07 m)(7.3 rad/s)

                                    = 0.51 m/s

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