a) Write an equation for the curve in the figure below that describes the motion

Question

a) Write an equation for the curve in the figure below that describes the motion of the mass oscillating on the spring as a function of time. Hint: Find the angular frequency, amplitude and phase angle. For the latter, you can discern it directly from the plot below.

b) Find the spring constant if mass attached to the spring is 3.5 kg.

c) Find the maximum speed the mass attains during its motion. At what x position does this max speed occur?

d) Find the magnitude of the maximum acceleration of the mass. At what TWO x positions does the mass endure this acceleration?

e) What is the maximum force the spring exerts on the mass?

Explanation / Answer

from the graph T = 4 s

w = 2pi/T = pi/2 = 1.57 rad/s

amplitude = A = 10 cm

x = A*cos(wt)

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b)

k = m*w^2 = 3.5*1.57^2 = 8.63 N/m

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c)

Vmax = A*w = 0.1*1.57 = 0.157 m/s

at x = 0

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d)

a = w^2*A = 1.57^2*0.1 = 0.25 m/s^2

at x = 10 cm

x = -10 cm

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e)

F = k*A = 8.63*0.1 = 0.863 N

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