Find the force on the ball  Â
F = m a
= ( 3.5 kg ) ( 5.00 m/s2)
=Â Â Â 17.50Â Â Â N
( a.)
As the ball is not oscillating, this must be equal to the
restoring force exerted by the spring.
   F   =   k x
Hence the maximum displacement (amplitude) of the
ball  Â
AÂ Â Â =Â Â Â F / k
=Â Â Â 17.50 / 227
= 0.0771 m
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(b) Expression for frequency:
f   =   (1/2π) √(k/m)
=   (1/2 * 3.14) √(227 / 3.5)
=Â Â Â 1.28 Hz
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( c) Expression for maximum velocity:
v   =   ω A
=   2 π f A
=   2 π ( 1.28 ) ( 0.0771 m)
=Â Â Â 0.621 m/s
   Thus, the maximum velocity relative to the
vehicle
   vmax = vvehicle + v
            =   45.0
+ 0.621 m/s
            =   45.62
m/s
