SOLUTION: The period of a particle moving in SHM is 6 seconds and its amplitude is 8cm. Calculate its velocity and acceleration to 1dp when the particle is 5cm from the centre of motion.

Question 1142816: The period of a particle moving in SHM is 6 seconds and its amplitude is 8cm. Calculate its velocity and acceleration to 1dp when the particle is 5cm from the centre of motion.
I currently have x=8cos(pi/3 t + alpha), but I'm not sure how to get alpha.
Answer by ikleyn(52847) (Show Source): You can put this solution on YOUR website!
.

By changing the origin for the time, you may forget about  and write the formula for SHM in the form


    x = .


It is totally enough to solve the problem.


Now, when x= 5 cm, you have  5 = , or


     = .


Next, the velocity is the DERIVATIVE of the position function x = x(t)


    Velocity = () = .


You just know the cosine function    from (1) - so you can calculate 

     = .


In this way, you can complete calculations for velocity.


Then for acceleration, use the fact that it is THE SECOND DERVATIVE of the position function and do the same.

At this point I completed my instructions.

Are they clear to you ?

If you still have difficulties/questions, let me know by posting your message through the "Thank you" window.

In this case, refer to the problems ID number, which is 1142816.
(otherwise, I will not to know to whom to answer).

Keep me informed about your progress.

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