Simple harmonic motion question

[i_heart_you]

Simple harmonic motion question!

Homework Statement

A mass undergoing simple harmonic motion has a displacement of X = 0.5 m and V = 4 m/s at one time and x=.25 and V = -8. what is the period of this oscillation?

Homework Equations

X(t) = Acos (wt + phi)
V(t) = -Awsin (wt + phi)

The Attempt at a Solution

 

[tiny-tim]

Hi i_heart_you!

(have a phi: φ and an omega: ω )

Show us what you've tried, and where you're stuck, and then we'll know how to help!

 

[kerimek]

To find the period of the oscillation, we can use the equation T = 2π/w, where T is the period and w is the angular frequency. We can find w by using the equation V(t) = -Awsin (wt + phi) and plugging in the given values of V and x at the two different times. This will give us two equations with two unknowns (w and phi). Solving for w in both equations and setting them equal to each other will give us the angular frequency w. Then, we can plug this value into the equation T = 2π/w to find the period of the oscillation.