Time period of a particle executing SHM is 16 s. At time , it crosses the mean position its amplitude of motion is m. Its velocity at is

Question

Time period of a particle executing SHM is 16 s. At time $t = 2 s$ , it crosses the mean position its amplitude of motion is $\frac{32 \sqrt{2}}{π}$ m. Its velocity at $t = 4 s$ is

Smart Achievers · Accepted Answer

(3)

$For SHM, x = A \sin ω t = A \sin (\frac{2 π t}{T}), v = ω \sqrt{A^{2} - x^{2}}$

$When t = 4 s, time taken by the particle to travel from the mean position to the given position = 4 - 2 = 2 s$

$x = A \sin (\frac{2 π t}{T}) = A \sin (\frac{2 π \times 2}{16}) = \frac{A}{\sqrt{2}}$

$v = ω \sqrt{A^{2} - x^{2}}$

$v = ω \sqrt{A^{2} - \frac{A^{2}}{2}} = \frac{ω A}{\sqrt{2}}$

$ω = \frac{2 π}{T} = \frac{2 π}{16} = \frac{π}{8}$

$∴$ $v = \frac{π A}{8 \sqrt{2}}$

Solution

Q.
Time period of a particle executing SHM is 16 s. At time $t = 2 s$ , it crosses the mean position its amplitude of motion is $\frac{32 \sqrt{2}}{π}$ m. Its velocity at $t = 4 s$ is

1 $1 m s^{- 1}$

2 $2 m s^{- 1}$

3 $4 m s^{- 1}$

4 $8 m s^{- 1}$

Want Us to Email you About Special Offers & Updates?

Solution

Q. Time period of a particle executing SHM is 16 s. At time t=2s, it crosses the mean position its amplitude of motion is 322πm. Its velocity at t=4s is

1 1 ms-1

2 2 ms-1

3 4 ms-1

4 8 ms-1