the acceleration a (in cm/s^2) at time t (in seconds) of a vibrating wire is given by a= -0.01 (1024pi)^2 cos1024πt.

Question

Determine the velocity v and position s at any time, if s=0.01 cm and v=0 cm/s at t=0s.

Answer 1

To calculate velocity, you must integrate the acceleration function with that initial condition. That is, perform

v = ∫ a dt

and determine the constant "C" from initial conditions.

Once you got the v-function, then do the same for the position,

s = ∫ v dt

where you would again determine the constant of integration using the initial conditions.

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