Question

If a SHM is represented by the equation x = 10
sin
$\pi t+ \frac{\pi}{6}$
in SI units, then what is its
maximum velocity?​

Answer 1

Answer:

Given:

Equation of SHM is given as :

x = 10 sin(πt + π/6)

To find:

Max velocity of the SHM.

Concept:

Max Velocity of the SHM is obtained at the mean position of the trajectory when the force acting on the particle is zero.

Mathematically,

$velocity = \omega \sqrt{ {A}^{2} - {x}^{2} }$

Now putting x = 0 (mean position)

$max \: v = \omega \sqrt{ {A}^{2} }$

$\boxed{\therefore \: max \: v = \omega \times A}$

Calculation:

Comparing with a standard Equation of SHM, we get :

$\boxed{x = A \sin( \omega t + \phi)}$

ω = π .............(1)

Now putting value of (1) in above Equation:

${\therefore \: max \: v = \omega \times A}$

$= > max \: v = \pi \times 10$

$= > max \: v = 10\pi$

$= > max \: v = 31.4 \: m {s}^{ - 1}$

So final answer :

$\boxed{ \red{ max \: v = 31.4 \: m {s}^{ - 1}}}$