(b) A light helical spring, for which the force necessary to produce unit extension is k, hangs vertically from a fixed support and .carries a mass M at its lower end. Assuming that Hooke's law is obeyed and that there is no damping, show that if the mass is displaced in a vertical. direction from its equilibrium position and released, the subsequent motion is simple harmonic. Derive an expression for the time period in terms of M and k.
(b) A light helical spring, for which the force necessary to produce unit extension is k, hangs vertically from a fixed support and .carries a mass M at its lower end. Assuming that Hooke's law is obeyed and that there is no damping, show that if the mass is displaced in a vertical. direction from its equilibrium position and released, the subsequent motion is simple harmonic. Derive an expression for the time period in terms of M and k.
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Transcribed Image Text:A108 (a) Define sinple harmonic motion.
(b) A light helical spring, for which the force
necessary to produce unit extension is k,
hangs vertically from a fixed support and
.carries a mass M at its lower end.
Assuming that Hooke's law is obeyed
and that there is no damping, show that
if the mass is displaced in a vertical
direction from its equilibrium position
and released, the subsequent motion is
simple harmonic. Derive an expression
for the time period in terms of M and k.
(c) If M = 0.30 kg, k= 30 N m ' and the
initial displacement of the mass is
0.015 m, calculate:
(i) the maximum kinetic energy of the
mass,
(ii) the maximum and minimum values
of the tension in the spring during
the motion.
(d) Sketch graphs showing how (i) the
kinetic energy of the mass, (i) the
tension in the spring vary with displace-
ment from the equilibrium position.
(c) If the same spring with the same nass
attached were taken to the Moon, what
would be the effect, if any, on the time
period of the oscillations? Explain your
answer.
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