Solve Spring Force Problem: Displacement, Velocity & Acceleration

[jybe]

Homework Statement

A spring of negligible mass stretches 3.00 cm from its relaxed length when a force of 6.30 N is applied. A 0.540-kg particle rests on a frictionless horizontal surface and is attached to the free end of the spring. The particle is displaced from the origin to x = 5.00 cm and released from rest at t = 0. (Assume that the direction of the initial displacement is positive. Use the exact values you enter to make later calculations.)

1) Determine the displacement x of the particle from the equilibrium position at t = 0.500 s.

2) Determine the velocity and acceleration of the particle when t = 0.500 s.

Homework Equations

[/B]
x = Acos(2pi*f*t)

v = -Aωsin(2pi*f*t)

a = -Aω^2cos(2pi*f*t)

Already found ω = 19.72 rad/s

frequency = 3.139 s^-1

The Attempt at a Solution

1)

x = 0.05*cos(pi*3.139)
x = 0.04926 m or 4.926 cm

2)

v = -0.05*19.72*sin(pi*3.139)
v = -0.168869 m/s

a = -0.05*(19.72)^2*cos(pi*3.139)
a = -19.1566 m/s^2

My answers for angular velocity and frequency are correct but apparently my answers for position, velocity and acceleration are wrong. Do I need my calculator in radians?

 

[haruspex]

Do I need my calculator in radians?

There was no need to find the frequency. You want cos(ωt), you found ω, and you are given t.
What are the units of ω? So what are the units of ωt?

 

[jybe]

There was no need to find the frequency. You want cos(ωt), you found ω, and you are given t.
What are the units of ω? So what are the units of ωt?

rad/s and rad. Are you saying I should use the same equations without frequency?

 

[haruspex]

rad/s and rad. Are you saying I should use the same equations without frequency?

I'm saying you do not need to find the oscillation frequency (f). You have the angular frequency, ω, and an equation that uses ω.
Since the units of the ωt you get will be radians, what mode do you think your calculator needs to be into find its cosine?

 

[jybe]

I'm saying you do not need to find the oscillation frequency (f). You have the angular frequency, ω, and an equation that uses ω.
Since the units of the ωt you get will be radians, what mode do you think your calculator needs to be into find its cosine?

Ah, thanks, I finally got the correct answer, but what do you mean I didn't have to find the oscillation frequency?

I feel a bit stupid to say this but the equations in my textbook are of the form: a = -Aω^2cos(2pi*f*t)

 

[haruspex]

the equations in my textbook are of the form: a = -Aω^2cos(2pi*f*t)

That's unusual.
The usual form is Acos(ωt), ω being the "angular frequency", along with period T=2π/ω and f=1/T is the oscillation frequency.

 

[neilparker62]

Ah, thanks, I finally got the correct answer, but what do you mean I didn't have to find the oscillation frequency?

I feel a bit stupid to say this but the equations in my textbook are of the form: a = -Aω^2cos(2pi*f*t)

Are you perhaps just missing or forgot $$ ω=2πf $$