Question

The equation of shm is y=10sin (10t -pi by 6)m calculate the frequency, time period, maximum velocity and acceleration.

Answer 1

$\huge\underline{\underline{\bf \orange{Question-}}}$

The equation of shm is ${\sf y = 10sin(10t-\dfrac{π}{6}}$ calculate the frequency, time period, maximum velocity and acceleration

$\huge\underline{\underline{\bf \orange{Solution-}}}$

Wave Equation ➝

y = A sin(wt - kt )m

On comparing with given Equation

A = Amplitude = 10m

$\omega$ = 10 rad/s

$\large\underline{\underline{\sf To\:Find:}}$

• Frequency
• Time period
• maximum velocity
• Acceleration

Frequency ➝

✪$\large{\boxed{\bf \blue{\omega = 2πf} }}$

$\implies{\sf 10=2π×f}$

$\implies{\bf \red{ f = \dfrac{5}{π}Hz}}$

Time period ➝

✪$\large{\boxed{\bf \blue{\omega =\dfrac{2π}{T}} }}$

$\implies{\sf T = \dfrac{2π}{10}}$

$\implies{\bf \red{Time(T)=\dfrac{π}{5}sec}}$

Maximum Velocity ➝

✪$\large{\boxed{\bf \blue{v =\omega A}}}$

$\implies{\sf v = 10×10}$

$\implies{\bf \red{Maximum\: velocity (v)=100m/s}}$

Acceleration ➝

✪$\large{\boxed{\bf \blue{a=\omega^2A} }}$

$\implies{\sf a = (10)^2×10 }$

$\implies{\bf \red{a = 1000\:m/s^2} }$

$\huge\underline{\underline{\bf \orange{Answer-}}}$

Frequency (f) = ${\bf\red{\dfrac{5}{π}Hz}}$

Time period (T) = ${\bf \red{\dfrac{π}{5}s}}$

Maximum velocity (v) =${\bf\red{100m/s}}$

Acceleration (a) = ${\bf\red{1000m/s^2}}$