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A 1.5-kg mass attached to spring with a force constant of 20.0 N/m oscillates on

ID: 2207967 • Letter: A

Question

A 1.5-kg mass attached to spring with a force constant of 20.0 N/m oscillates on a horizontal, frictionless track. At t=0, the mass is released from rest at x= 10.0 cm. (That is, the spring is stretched by 10.0cm). a- determine the frequency of the oscillations. b- Determine the maximum speed of the mass. Where does the maximum speed occur? c-Determine the maximum acceleration of the mass. Where does the maximum acceleration occur? d- Determine the total energy of the oscillating system. e- Express the displacement as a function of time.

Explanation / Answer

let the oscillations be described by the following relation,
x=Asin(t+)

where, x =postion , A= amplitude , =k/m , =phase difference

=3.65

x = 10sin(3.65t+/2)

a. F= /2 = 3.65/2 = 0.5811 Hz

b. v=dx/dt = Acos(t+)

max speed= A = 3.65x10 = 36.5 cm/s

x= 0 cm

c.accleration= dv/dt

dv/dt= -2Asin(t+)

max a = -2A = 133.225cm2/s

d. total energy= 1/2 k (0.01) = 0.1 J

e. x = 10sin(3.65t+/2)