Problem1 At what point during the oscillation of a
spring is the force on the mass greatest?
Solution: Recall that F = - kx . Thus the force on the
mass will be greatest when the displacement of the
block is maximum, or when x = ±xm .
 Problem2 : What is the period of oscillation of a
mass of 40 kg on a spring with constant k = 10 N/m?
Sol:
m
40
T  2
 2
 2
 4   S

k
10
 Notice that period, frequency and angular frequency
are properties of the system, not of the conditions
placed on the system.
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 Problem3 : A mass of 2 kg is attached to a spring with
constant 18 N/m. It is then displaced to the point x = 2
. How much time does it take for the block to travel to
the point x = 1 ?
 Solution:
For this problem we use the sin and cosine equations
we derived for simple harmonic motion.
Recall that x = xm cos(wt) . We are given x and xm in
the question, and must calculate w before we can
find t .   k  18  3
m
2
x = xm cos(wt), 1=2 cos(3t),,,, t = 0.35 sec
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 Problem 4: A mass of 2 kg oscillating on a spring
with constant 4 N/m passes through its equilibrium
point with a velocity of 8 m/s. What is the energy of
the system at this point? From your answer derive
the maximum displacement, xm of the mass.
K 
1
1
mv 2   2  82  64
2
2
joules
Since this is the total energy of the system, we can use this answer
to calculate the maximum displacement of the mass. When the
block is maximally displaced, it is at rest and all of the energy of the
system is stored as potential energy in the spring, given by U = 1/2
kxm2 , Since energy is conserved in the system, we can relate the answer
we got for the energy at one position with the energy at another:
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Since energy is conserved in the system, we can relate the answer we got for
the energy at one position with the energy at another:
1 2 1 2
kx m  mv  64 joules
2
2
xm 
2  64
2  64

 16  4 meters
k
8
5- A 200-g block is attached to a horizontal spring and •
executes simple harmonic motion with a period of 0.250 s. If
the total energy of the system is 2.00 J, find (a) the force
constant of the spring and (b) the amplitude of the motion.
6- A block–spring system oscillates with an amplitude of
3.50 cm. If the spring constant is 250 N/m and the mass of
the block is 0.500 kg, determine (a) the mechanical energy
of the system, (b) the maximum speed of the block, and (c)
the maximum acceleration.
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