# Thread: Differentiation Problem

1. ## Differentiation Problem

1. If the equation of motion of a particle is given by s = B cos(ωt + δ), the particle is said to undergo simple harmonic motion. Find the velocity.

Answer: v(t) = -Bwsin(wt + δ)

2. When is the velocity = 0?

Can you please show me step-by-step how to find when the velocity = 0? Thanks.

2. You need to solve $\displaystyle v(t) = -B \omega sin( \omega t + \delta) = 0$ for $\displaystyle t$.

Since you assume the particle is moving in harmonic motion, having $\displaystyle B=0$ or $\displaystyle \omega = 0$ would contradict that -- so you can safely assume that $\displaystyle B, \omega \neq 0$. Now all you have to solve is $\displaystyle sin( \omega t + \delta) = 0$

3. Originally Posted by Maziana
1. If the equation of motion of a particle is given by s = B cos(ωt + δ), the particle is said to undergo simple harmonic motion. Find the velocity.

Answer: v(t) = -Bwsin(wt + δ)

2. When is the velocity = 0?

Can you please show me step-by-step how to find when the velocity = 0? Thanks.
The velocity is equal to zero when
$\displaystyle \sin(\omega t+\delta)=0$

$\displaystyle \omega t +\delta =\sin^{-1}(0)$

$\displaystyle t=\frac{\sin^{-1}(0) -\delta}{\omega}$