1. 1. A spring has a spring constant k = 0.69 N/m. It is stretched 0.30 m from i
ID: 1414588 • Letter: 1
Question
1. 1. A spring has a spring constant k = 0.69 N/m. It is stretched 0.30 m from its equilibrium position. Give the formula for the restoring force of the spring. Calculate the restoring force of the spring. (Give your answer to 2 significant figures.)
2. An object of mass M = 4.5 kg is suspended from a spring of spring constant k = 2.27 N/m. Give the formula for the displacement of the end of the spring due to the weight of the mass. Calculate the displacement of the end of the spring due to the weight of the mass. (Give your answer to 2 significant figures.)
3. Write the mathematical equation that shows connection between angular frequency and period of oscillations?
4. The sample of the position vs time graph produced by a 550 grams card going into the SHM is provided below. The amplitude of the oscillations (parameter A) is 0.0809 m on the position vs time graph. The period of the oscillation (parameter B) is 0.571 s. Based on this experimental data calculate:
a) the angular frequency of oscillation; b) the spring constant of the system; c) maximum potential energy that stored in the system.
Explanation / Answer
(1)
F = kx = 0.69(0.3) =0.207 N
(2)
F= kx
mg = kx
x = mg/k = 4.5 ( 9.8)/2.27
=19.42 m
(3)
w = 2pi/T
(4)
(a)
w = 2pi/T = 2pi/0.571 s =10.99 rad/s
(b)
k = w^2 m ( 10.99)^2 ( 0.550) = 66.52 N/m
(c)
PE = 1/2 k A^2 = 1/2 * 66.52 ( 0.0809) ^2 = 0.217 J
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