Question

How can I calculate maximum velocity in simple harmonic motion?

Answer 1

In this type of questions, to get the formula for calculating maximum velocity, first the formula for velocity should be known and then since simple harmonic motion is related to waves, which has amplitude, wavelength, etc. so from the wave we can know the point where velocity will be maximum and the corresponding value of other variable at that point, which when substituted in the formula for velocity will give the formula for maximum velocity.
Formula used:
$v=\omega \sqrt{{{A}^{2}}-{{y}^{2}}}$

Complete answer:
In Simple Harmonic Motion, we know that velocity can be found using the formula,
$v=\omega \sqrt{{{A}^{2}}-{{y}^{2}}}$
where,
$\begin{aligned} & \omega =\text{Angular Frequency} \\\ & A=\text{Amplitude} \\\ & y=\text{Displacement} \\\ \end{aligned}$
Now, we know that velocity is maximum when $y=0$, i.e., displacement is zero and acceleration is zero, which means the system is in equilibrium.
So, substituting the value of y in equation, we get:
$\begin{aligned} & v=\omega \sqrt{{{A}^{2}}-{{0}^{2}}} \\\ & \Rightarrow v=\omega \sqrt{{{A}^{2}}} \\\ & \therefore v=A\omega \\\ \end{aligned}$
Therefore, at a point in simple harmonic motion, the maximum velocity can be calculated using the formula $v=A\omega$.

Additional Information:
In mechanics and physics, simple harmonic motion is a special type of periodic motion where the restoring force on the moving object is directly proportional to the object's displacement magnitude and acts towards the object's equilibrium position. It results in an oscillation which, if uninhibited by friction or any other dissipation of energy, continues indefinitely.

Note:
Simple Harmonic Motion is an important topic in physics and the questions on it are also easy to solve. The main information that is needed to solve this kind of problem can be obtained from the wave that is created by this motion. In SHM, the formula for getting the equation of wave is mainly dependent on amplitude, wavelength, angular frequency, and angle of the wave.