# Simple Harmonic Motion and waves: Velocity and acceleration

Please help with 14, 15 and 16 with step by step solutions showing equations used and answers.

answer 14 not 16.1cm, answer 15 not 8.123 m/s, answer 16 not 19.6 m/s^2.

(See attached file for full problem description)

© BrainMass Inc. brainmass.com December 24, 2021, 5:43 pm ad1c9bdddfhttps://brainmass.com/physics/acceleration/simple-harmonic-motion-waves-velocity-acceleration-64551

## SOLUTION This solution is **FREE** courtesy of BrainMass!

Please see the attachment.

Please do 14, 15 and 16 with step by step solutions showing equations used and answers. Please show all steps and thnaks for help.

answer 14 not 16.1cm, answer 15 not 8.123 m/s, answer 16 not 19.6 m/s^2.

Answer 14.

The oscillator is completing 43 vibrations in 20.4 s hence the frequency of the oscillator i.e. the number of oscillations completed in one second is given by

n = 43/20.4 = 2.1078 Hz

The frequency of the wave is the same as that of the oscillator.

The wave velocity is the distance covered by the wave in one second. As the distance covered by the particular crest in 12.4 second is 420 cm hence the wave velocity is given by

c = 420/12.4 = 33.871 cm/s

Now as we know that the wavelength, wave velocity and the frequency is related as

c = n where is the wavelength, hence

= c/n = 33.871/2.1078 = 16.069cm = 0.16069 m.

-----------------------------------

Answer 15.

This function represents the motion of a particle of medium. When wave travels through a medium, the particles of the medium oscillate. During the oscillation the displacement of a particular particle is given by this equation.

x = A cos t.

where A is called the amplitude of oscillation and is angular frequency.

The velocity of this particle can be obtain by differentiating above equation with respect to the time, hence

v = dx/dt = - Asin t = -3.1*27 sin(27*9.5) = - 83.7 sin(256.5rad)

= - 83.7*(-0.896) = 74.99 = 75 m/s

Here t is 256.5 rad = 81.646 rad which is equivalent to 82 - 0.354 radians

Equivalent to - 63.720 and sin(-63.720) = - 0.896

--------------------------------------------

Answer 16

The acceleration of the particle is given by

a = dv/dt = = - 3.1*272 cos(-63.720)

= - 2259.9*0.4427 = - 1000.4 m/s2.

-------------------------------------

may clear and confusion through Brainmass.

https://brainmass.com/physics/acceleration/simple-harmonic-motion-waves-velocity-acceleration-64551