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Answer :
Answer:(a) the maximum stretch of the spring is 17.7cm.
(b) the maximum speed during the motion is 4.08 m/s.
(c) the average power input required is 0.11W.
Spring-mass system:
(a) The law of conservation of energy suggests that the total mechanical energy of the system remains conserved in case of a constant or conservative force. So,
the initial energy of the spring-mass system = final energy
also, the total energy remains conserved, so, when the potential energy is maximum, the kinetic energy is zero.
where, u = 3 m/s is the initial speed of the mass m = 0.3kg
k = 160 N/m is the spring constant and x = 12cm = 0.12m is the initial displacement of the spring and A is the maximum displacement of the spring.
(b) when the speed is maximum, the kinetic energy is maximum, so the potential energy must be zero, then:
where v is the maximum speed.
(c) the energy dissipated per cycle is 0.03 J which is equal to the work done by the system W. The average power is defined as the rate of work.
So the average power P per cycle is :
P = W/T
where T is the time period of oscillation given by:
So,
P = 0.11 W
Explanation:
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