1- An object attached to a spring exhibits simple harmonic motion with an amplit

Question

1- An object attached to a spring exhibits simple harmonic motion with an amplitude of 12 cm. How far from equilibrium will the object be when the system's potential energy is equal to its kinetic energy?

.. 5.00 cm

.. 8.49 cm     

.. 9.00 cm

.. The distance can't be determined from the data given.

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2- Two mass-spring systems oscillate with periods TA and TB. If TA = 2TB and the systems' springs have identical force constants, it follows that the systems' masses are related by

.. mA = 4mB

.. mA = mB/2     

.. mA = mB/2

.. mA = mB/4

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3- A 0.110-kg block is suspended from a spring. When a small pebble of mass 31 g is placed on the block, the spring stretches an additional 4.9 cm. With the pebble on the block, the block oscillates with an amplitude of 14 cm. Find the maximum amplitude of oscillation at which the pebble will remain in contact with the block.
..... cm

Explanation / Answer

given,

amplitude = 12 cm

if KE = PE then

PE = total mechanical energy / 2

total mechanical energy = 0.5 * k * 12^2

PE = 0.5 * k * 12^2 / 2

PE = 0.5 * k * x'^2

x'^2 = 12^2 / 2

x' = 8.49 cm

it has to be 8.49 cm far

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