A system consisting of a small 1.20-kg object attached to a light spring oscilla

Question

A system consisting of a small 1.20-kg object attached to a light spring oscillates on a smooth, horizontal surface. A graph of the position x of the object as a function of time is shown in the figure below, t = 0.28 s. Use the graph to answer the following questions. What is the angular velocity w_0 of the motion? (Express your answer to two significant figures.) rad/s What is the angular frequency of the motion? (Express your answer to two significant figures.) rad/s What is the spring constant of the spring? (Express your answer to two significant figures.) kg/s^2 What is the maximum speed of the object? (Express your answer to two significant figures.) m/s What is the maximum acceleration of the object? (Express your answer to two significant figures.) m/s^2

Explanation / Answer

mass of the object, m=1.2kg

and

time t=0.28 sec

from the graph,

time period, T=2*t

T=2*(0.28)

T=0.56 sec

1)

anguar velocity , W=2pi/T

W=2pi/0.56

W=11.22 rad/sec

2)

angular frequency, W=2pi/T

W=11.22 rad/sec

3)

T=2pi*Sqrt(m/K)

0.56=2pi*sqrt(1.2/k)

===> K=151.06 N/m

spring constant, K=151.06 N/m

4)

maximum speed Vmax=A*w

here,

amplitude, A=4cm

==>

Vmax=0.04*11.22

Vmax=0.45 m/sec

5)

maximum acceleration,

a=w^2*A

a=11.22^2*(0.04)

a=5.03 m/sec^2

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