Question

The tip of one prong of a tuning fork undergoes SHM of frequency 936 Hz and amplitude 0.717 mm. For this tip, what is the magnitude of the (a) maximum acceleration, (b) maximum velocity, (c) acceleration at tip displacement 0.232 mm, and (d) velocity at tip displacement 0.232 mm

Answer 1

given,

frequency of tuning fork = 936 Hz

Amplitude = 0.717 mm

a) The maximum acceleration is given by

`a_(max)= \omega^2 x_(max)`

`a_(max)= (2\pi f)^2 x_(max)`

`a_(max)= 4 \pi^2 f^2 x_(max)`

`a_(max)= 4 \pi^2 936^2 * 0.717 * 10^(-3)`

`a_(max)=2.48 * 10^4 \ m/s^2`

b) maximum velocity

`v_(max)= \omega\ x_(max)`

`v_(max)= 2\pi f y_(max)`

`v_(max)= 2\pi * 936 * 0.717 * 10^(-3)`

`v_(max)=4.22\ m/s`

c) displacement =y = 0.232 mm

`a_(max)= \omega^2 y_(max)`

`a_(max)= (2\pi f)^2 y_(max)`

`a_(max)= 4 \pi^2 f^2 y_(max)`

`a_(max)= 4 \pi^2 936^2 * 0.232 * 10^(-3)`

`a_(max)=8.024 * 10^3 \ m/s^2`

d) velocity at y = 0.232 mm

`v_(max)= \omega\sqrt{x_(max)^2-y^2}`

`a_(max)= 2\pi f\sqrt{x_(max)^2-y^2}`

`a_(max)= 2\pi * 936 * \sqrt{(0.717 * 10^(-3))^2-(0.232 * 10^(-3))^2}`

`a_(max)=3.989\ m/s`