Question

Can anyone help with the following question:
assuming x(t)=X sin wt and initial conditions are x=0mm and v=1.5m/s, find a) the amplitude of the vibrations? b) the expression for acceleration at any time x(t)?

Answer 1

x(t) = Asin(ωt + φ).
v(t) = dx(t)/dt = ωAcos(ωt + φ),
a(t) = dv(t)/dt = -ω^2Asin(ωt + φ) = -ω^2*x and the amplitude is A

Answer 2

Thanks ghazi still a little confused tho....

Answer 3

where is the confusion now?

Answer 4

I have amended the Question they actually ask it x(t) = X Sin wt does X still refer to the amplitude?

and when they ask us to find the expression for acceleration there is double dot about the X(t) i can only assume that that is the second derivative that you have shown me above?

Answer 5

X is the amplitude of the vibrations....where x(t) is the function that describes the variation of that vibration ....and to find out acceleration you just need to differentiate it twice

Answer 6

Thanks alot ghazi, the text i have is not very user friendly!!!! they have changes symbols around terribly laid out!!!!!!

Answer 7

welcome...hope it is clear now... :)

Answer 8

got it

Answer 9

The dot means the derivative with respect to time.