Simple Harmonic Motion with Initial Velocity: Calculating Speed and Time Period

[SherlockOhms]

Homework Statement

(b) A particle is projected from a point O at time t = 0 and it performs simple harmonic
motion with O as a centre of oscillation. The motion is of amplitude 20cm and time period
4 seconds.
Find:
(i) the speed of projection;
(ii) the speed of particle when t = 1:5 seconds;
(iii) the time when the particle is rst at a point 10cm from O.
x(0) = x0; x'(0) = v0:

Homework Equations

v = ωr.
T = 2pi/ω

The Attempt at a Solution

For part (i) is it it correct to assume that the initial velocity is the velocity through the centre of motion? In that case, would the speed of the projection v0 = ωr, where r is the amplitude and ω can be found using 2pi/T?

 

[gneill]

For part (i) is it it correct to assume that the initial velocity is the velocity through the centre of motion? In that case, would the speed of the projection v0 = ωr, where r is the amplitude and ω can be found using 2pi/T?

Sure, sounds good.

 

[SherlockOhms]

Thanks for that.