Finding frequency, period and velocity from displacement equation

[bard]

A particle has displacement given by$$x=3.0\cos(5\pi t+\pi)$$ where x is in meters and t in seconds

A)What are the frequency ,F, and the period,T, of motion
B)What is the greatest distance the particle travels from equlibrium
c)Where is the particle at time t=0?t=0.5(s)
D)What is the velocity when t=0.5s

A)F=2.5, T=0.4
B)3.0M
c)3.0M
d)no idea

thank you

 

[himanshu121]

Apply the formula for velocity i.e dy/dx

 

[bard]

I have no idea what you are talking about? are my other answers correct?

 

[himanshu121]

d)no idea

Others are correct i thought you need to calculate the velocity
dont u

 

[bard]

yes i need to calculuate velocity, but i don't know how to get it.

 

[himanshu121]

Look you got the displacement, Pls tell yourself what is the relation between displacement and velocity

 

[bard]

ok so i have to take the derivative

$$x=3.0\cos(5\pi t+\pi)$$

so the derivative of that would be

$$3.0*-\sin(5\pi(0.5)+\pi)*d/dx(5\pi(0.5)+\pi$$

 

[himanshu121]

Yes You got it right

 

[bard]

yes but i get v=0 when i do the derivative. is this correct?

thnx for ur help

 

[himanshu121]

Sorry U didn't write correctly

$$3.0*-\sin(5\pi(0.5)+\pi)*d/dx(5\pi(0.5)+\pi$$

it should be
$$3.0*-\sin(5\pi(0.5)+\pi)*d/dt(5\pi(0.5)t+\pi$$

I want to correct myself

Apply the formula for velocity i.e dy/dx

the velocity is time derivative
i.e v = dx/dt.

i just wanted to point towards the calculus involved

 

[bard]

thnx a lot man