A 4-kg mass is connected to a light spring (k = 25 N/m). The mass is pulled out

Question

A 4-kg mass is connected to a light spring (k = 25 N/m). The mass is pulled out 15 cm from its equilibrium position, and released at t = 0. Once the mass is released, it begins oscillating in SHM. During the subsequent oscillations: The position of the mass is described by x(t) = x_m cos (omega t): What are the values of x_m and omega? How many oscillations will this mass complete in one minute? What is its maximum speed? What is its maximum acceleration? What is its maximum kinetic energy? What is the system's mechanical energy (E = K + U)? What was its position x at t = 2.0 s? What is its speed when x = 5 cm?

Explanation / Answer

1)
w = sqrt (k/m)
= sqrt (25/4)
= 2.5 rad/s

xm = maximum amplitude = 15 cm = 0.15 m

2)
w = 2*pi/T
T = 2*pi/w
= 2*pi/2.5
=2.513 s

number of oscillation in 1 minute = 60 s/T
= 60/2.513
=23.9
= 24 oscillation approximately

3)
vmax = xm*w
=0.15*2.5
= 0.375 m/s

4)
a max = w^2*xm
= (2.5)^2 * 0.15
=0.9375 m/s^2

I am allowed to answer only 4 parts at a time

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