A spring with a spring constant of 65 N/m is attached to a 0.3 kg mass. Each cyc

Question

A spring with a spring constant of 65 N/m is attached to a 0.3 kg mass. Each cycle the mass travels a distance of 5.7 cm between its top and bottom extreme positions. Assume the mass starts at its top position.

I have already found the the frequency of vibration: 2.34Hz, the angular frequency of vibration: 14.7196 rad/sec, and the period of vibrations: 0.43 sec. However, I need help finding d) What is the amplitude of vibration?

e) Write down the math expressions for position, velocity and acceleration as a function of time. (i.e. s=?, v=?, a=?)

s(t) =

v(t) =

a(t) =

f) What is the size of the maximum velocity of the mass?

g) What is the size of the maximum acceleration of the mass?

and i) What is the expression for the force acting at any time on the spring?

Explanation / Answer

s(t) =ACoswt

v(t) =-AwSinwt

a(t) =-Aw^2Coswt

the size of the maximum velocity of the mass = wA = 14.7196*0.057/2 = 0.4195 m/s

the size of the maximum acceleration of the mass = w^2A = 6.175 m/s^2

the expression for the force acting at any time on the spring = -mAw^2Coswt

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