00:01
Hi, this question says the amplitude of a particle executing simple harmonic motion with a frequency of 60 harch is 0 .01 meter.
00:12
Okay, so the amplitude is given.
00:14
First, we will write down all the information given.
00:18
Amplitude given 0 .01 meter.
00:23
Clear? next, the frequency is given obviously.
00:27
The linear frequency is given.
00:30
60 harts and the maximum value of acceleration of the particle is asked that is a max that is the acceleration maximum acceleration okay in this simple harmonic motion so there is a particle that executes a simple harmonic motion so now what is the wave equation for this simple harmonic motion first we have to know this this question is based on wave and oscillation so the equation of the displacement of a particle, the equation of the displacement of a particle that executes that executes simple harmonic motion.
01:18
Okay.
01:19
Suppose along x -axis.
01:21
Suppose along x -axis the particle is moving.
01:25
Okay.
01:26
That means the direction of propagation is along x -axis.
01:30
So the displacement will be along x axis.
01:33
So we will write down the equation by taking x clear a sign omega t.
01:40
So it's a waveform of sinusoidal wave.
01:43
Okay, sinusoidal wave.
01:44
That's why we have taken a sine omega t where a is the amplitude of the wave, right? amplitude.
01:51
See already we have written amplitude that means 0 .01.
01:56
Clear? next frequency is f that is.
02:00
Given 60 harts but see in this equation there we have written omega that is omega is the angular frequency that is equal to 2 pi f omega is equal to 2 pi f right now we have to find out the maximum acceleration for that this is the differential equation so for that first we have to derive this equation with respect to time to get the velocity of the wave so how to find out velocity that will be d x by d t that means first order derivative of this differential equation okay this is function of t clear so now a sine omega t so what will be the differentiation that will be a omega cos omega so this is the velocity now we have to find out the acceleration so what about acceleration as we know that acceleration is equal to changing velocity with respect to time that means the derivative we have to find out that is the first order derivative of velocity equation with respect to time.
03:03
Right...