Waves Practice Problem Set Worksheet Page 11
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ECHANICS
RACTICE
ROBLEM
ETS
7.4.2 Mass-Spring System
1. When a family of four with a total mass of 200 kg gets into their 1200 kg car, the
car’s springs compress 5 cm. What is the spring constant of the car’s springs
assuming they act as one single spring?
Answer: 39,200 N/m
2. Imagine that you videotape the motion of a mass attached to a spring and measure the
displacement x from the equilibrium position as a function of time t. When you plot
position, velocity and acceleration as a function of time you get the following graphs.
a. Find the amplitude.
b. Find the period.
c. Find the angular frequency.
Answer: ω = 4 rad/s
d. Find the magnitude of the maximum velocity.
e. Find the magnitude of the maximum
acceleration.
3. When a 0.50 kg-object is attached to a vertically supported spring, it stretches 0.10 m.
It is then pulled another 0.10 m from its new equilibrium position. Find the period,
angular frequency, total energy, and displacement equation for this mass-spring
system.
Answer: T = 0.63 sec,
ω = 9.9 rad/s,
E
= .25 J,
T
x(t) = 0.10 cost (9.9t)
4. An object with mass m = 0.60 kg attached to a spring with k = 10 N/m vibrates back
and forth along a horizontal frictionless surface. If the amplitude of the motion is
0.050 m, what is the velocity of the object when it is 0.010 m from the equilibrium
position?
Answer: 0.20 m/s
Gamzon & Gregorian-Michaelsen
6/7/16
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