Question

A machine part is undergoing SHM with a frequency of 5.00Hz and amplitude 1.80cm . How long does it take the part to gofrom x=0 to x= -1.80 cm

Answer 1

Concepts and reason

The concepts used to solve this problem are displacement and time taken for a simple harmonic motion.

The machine part is undergoing simple harmonic motion.

Use the expression for the displacement of the simple harmonic motion to find the time taken for the displacement in the interval $x=0 $ to .

Fundamentals

In simple harmonic motion velocity is constantly changes, oscillating just as the displacement does.

Simple harmonic motion is the periodic motion in which restoring force is directly proportional to the displacement.

The time period is the time required for one oscillation.

Expression for the displacement of the object in simple harmonic motion is,

Here, is the displacement, is the amplitude, is the frequency, and is the time.

Amplitude is the maximum displacement from the equilibrium position.

Expression for the displacement of the object in simple harmonic motion is,

At the initial position, the value of is zero.

Substitute for and for .

Here, is the time when $x=0 $.

From the above expression,

Expression for the displacement of the object in simple harmonic motion is,

At the final position, the value of is .

Substitute for , for , and for .

Here, is the time when .

Expression for the time taken for the displacement in the interval $x=0 $ to is,

Here, is the time taken for the displacement in the interval $x=0 $ to .

Substitute for and for .

Substitute for .

Therefore, the time taken for the displacement in the interval $x=0 $ to is .

Ans:

The time taken for the displacement in the interval $x=0 $ to is .