Question

**Please do not write in handwriting**

1- Compare the values of kinetic, potential and total energy of an oscillating mass-spring system in the following cases:

a) When the spring is the most compressed and the most extended.

b) When the spring is nearly relaxed.

2- Suppose that a simple pendulum is calibrated to 2 cycles per second at sea level and is then brought up to the top of a tall mountain. What would need to be done to re-calibrate the pendulum at the top of the mountain?

3- An object of mass m is attached to a horizontal spring, stretched to a displacement A from equilibrium and released, undergoing harmonic oscillations on a friction-less surface. The experiment is then repeated with a mass of 4m, what change will happen to:

a) Periodic time.

b) Maximum speed of the mass.

c)Total energy

Answer 1

Ans.

1a.) When the spring is the most compressed and the most extended, the speed of the mass = 0 m/s So all the energy of the system is stored as the elastic potential energy.

So Potential energy = Total energy of the system and KE of the mass= 0 J

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1b.) When the spring is nearly relaxed, the elastic potential energy of the system is zero. Hence by energy conservation, total energy of the system is converted to kinetic energy of the mass.

Potential energy = 0J and Total energy = KE of the mass.

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