Question

A 0.30-kg block of wood is suspended on a spring. In equilibrium the wood stretches the spring 2.0 cm downward. The wood is then pulled an additional distance of 1.0 cm down and released from rest. How long does it take the wood to make 3 complete cycles of vibration? How much total mechanical energy does this system contain if we choose the total potential energy (elastic and gravitational) to be zero at the equilibrium position of the hanging block?

Answer 1

from the Hook's law

mg = kx

0.3 ( 9.8) = k (2 * 10^-2)

K = 147 N/m

period of spring mass system is

T =2pi sqrt m/k

= 2pi sqrt 0.3/147

=0.2837 s

for 3 comple cycles of vibration

T = 3 (T) = 3 ( 0.2837) = 0.8511 s

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(b)

E = 1/2 * K A^2

= 1/2 * 147 ( 1.0 * 10^-2)^2

=0.00735 J