Simple harmonic motion and maximum speed

[sauri]

I got a question, what is the maximum speed of an object undergoing SHM? and what is the max. acceleration.

I am not sure how to solve this without any data given. I know that velocity v=-Awsinwt. and acceleration is a=Awcoswt.
So how am I to find the max speed and max acceleration?. Pls help.

 

[nrqed]

I got a question, what is the maximum speed of an object undergoing SHM? and what is the max. acceleration.

I am not sure how to solve this without any data given. I know that velocity v=-Awsinwt. and acceleration is a=Awcoswt.
So how am I to find the max speed and max acceleration?. Pls help.

The max acceleration is - A \omega^2 cos (\omega t).

Well, what is the max acceleration you could get if you can use any time you want? That will be when the cos is equal to minus 1! (the max and min values of a cosine function are +1 or -1. Because of the overall minus sign, the acceleration will be maximum when the cosine function is minimum...which is when it is -1). When the sine is -1, what is the value of the acceleration? That's your answer.

The velocity will be max when the sine function is minimum...

 

[Hootenanny]

Alternatively, to find the maximum speed, you can use conservation of energy.