1. A 15.5 kg mass vibrates in simple harmonic motion with a frequency of 18.53 H

Question

1. A 15.5 kg mass vibrates in simple harmonic motion with a frequency of 18.53 Hz. It has a maximum displacement from equilibrium of +16.4 cm at time, t = 0.00 s. The displacement from equilibrium of the mass at time, t = 1.25 s is      cm

2.

                                       An unknown mass is hung from a very light spring with a spring constant of 20.4 N/m. Neglect the mass of the spring. If the period of oscillation of the mass-spring system is 3.11 s, then the unknown mass is      kg.

3. A ball of mass 1.95 kg is hung from a spring which stretches a distance of 0.5975 m. The spring constant of the spring (a scalar quantity) is      N/m

4.  When an object is in simple harmonic motion and is moving in the vertical direction, the magnitude of its acceleration is at a minimum when it _______.

is at the highest point is at the equilibrium point       is at either endpoint is at the lowest point

5. Hooke's Law is defined through the equation _______.

Explanation / Answer

1)

frequency = 18.53Hz

w = 2*pie*f = 2*3.14*18.53 = 116.36

equation of motion is 16.4cos(116.36t)

y at t= 1.25s is

y = 16.4cos(116.36*1.25) = 9.63 cm

2)

T = 2*pie*sqrt(m/k)

3.11 = 2*3.14*sqrt(m/20.4)

mass = 5 kg

3)

mg = kx

k = 1.95*9.8/0.5975 = 32 N/m

4) at the equilibrium point

5) F = -kx

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