Example Problems for Ch. 4.5Ch.4 end, Doug Smith, 10/27/2009
1. A 5 kg object is attached to a spring with spring (force) constant 160 N/m so that the object
is allowed to move on a horizontal frictionless surface. The object is released from rest
when the spring is compressed 0.3 m. Find the acceleration in m/s/s at that instant.
The equation of motion is F=ma=kx
In the problem x=0.3 m (spring is compressed (x direction) by 0.3 m)
Solve for a=kx/m=(160)(0.3)/(5)=9.6 N
(+ means in the +x direction)
2. Suppose you have a mass m hanging from a spring of spring constant k. The displacement is x and
time is t. In addition to the force exerted by the spring, you also have the force of gravity. Neglecting any
friction, what is the equation of motion for the mass? What is the solution to the equation of motion?
3. Suppose you have a simple mass spring system. The mass is m=4 and the spring obeys
Hooke's law and has a spring constant k=2. Ignore any effects of friction or gravity.
Suppose the initial displacement is x=3 and the initial velocity v=0. What is the change in velocity after a
small time step of 0.01 seconds?
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 Fall '10
 Smith
 Force, Friction, Mass

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