Question

A mass m is attached to an ideal massless spring. When this system is set in motion with amplitude a, it has a period t. What is the period if the amplitude of the motion is increased to 2a?.

Answer 1

The period remains the same if the amplitude of the motion is increased to 2a

What is Time period?

The time period is the time taken by a complete cycle of the wave to pass a point.

The equation of the period for spring is:

$T = 2\pi \sqrt{\frac{m}{k} }$

Where,

Time period = T  

mass of system = M

k is the spring constant

Amplitude of the motion is a

From the equation we can say that,

The period of a spring-mass system is proportional to the square root of the mass and inversely proportional to the square root of the spring constant.

Now if we increase the amplitude of the motion to 2a, the period of time remains the same.

Because the time period is not dependent on amplitude, it is independent of a.

Hence,

The period remains the same if the amplitude of the motion is increased to 2a.

Learn more about period of spring here:

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