Solve Oscillation Problem: |v|=0.5v_max

[phat2107]

Homework Statement

A block attached to a spring is displaced from equilibrium to the position x = +4.9 m and released. The period is 0.5 s . At what positions and times during the first complete cycle do the following condition occur:

| v | = 0.5 v_{max}, Where v_{max} is the maximum speed?

Homework Equations

none i suppose.

The Attempt at a Solution

I believe the s(t)= 4.9 sin (4pi(t)+0.5pi)
v(t) = 19.6pi cos (4pi(t)+0.5pi)

there for 0.5 max velocity is = 9.8pi ---> (19.6pi/2)

so for velocity without breaking the phase constant:

4pi (t) + 0.5pi = pi/3 5pi/3

i don't think i am right, can anyone clear it up?

 

[tiny-tim]

Hi phat2107!

Yes, that looks ok … |v| is half v_max when |cos| = 1/2 …

so that's when t and s = … ? ​