Question

A particle x A cos(wt-). The maximum velocity of the executing the motion is particle is​

Answer 1

question ---> A particle x A cos(wt). The maximum velocity of the executing the motion is particle is

A particle is executing simple harmonic motion such that displacement of particle is given by $x=Acos(\omega t)$ here A is amplitude, w is angular frequency.

we know, velocity is the rate of change of displacement with respect to time.

so differentiate x with respect to time, we get, $\frac{dx}{dt}= v =\omega Acos(\omega t)$

for maximum velocity , cos(wt) should be maximum, and we know maximum value of cosine is 1

then, maximum velocity of particle , $v_{max}=\omega A$