Forced Oscillations Homework: Determine Period & Amplitude

[Husker70]

Homework Statement

A 2.00 kg object attached to a spring moves without friction and is driven
by an external force F=(3.00N) sin(2pie t). Assuming that the force
constant of the spring is 20.0 N/m determine (a) the period and
(b) the amplitude of the motion.

Homework Equations

T = 2pi sqrrt(m/k)
A = (Fo/m)/sqrrt (w^2 - wsubO)^2

The Attempt at a Solution

T = 1.99s
A = ?

I don't think that either equation is right. The answers are in
the book but these aren't working.
Thanks,
Kevin

 

[Redbelly98]

There are 2 periods, or frequencies, of relevance here: the natural frequency, and the driving-force frequency.

If your calculated period is wrong, perhaps you need to think about the other period that is relevant.

 

[thomate1]

Based on the given information, the period and amplitude can be determined using the equations T = 2π√(m/k) and A = (F0/m)/√(ω^2 - ω0^2), where m is the mass of the object, k is the force constant of the spring, F0 is the amplitude of the external force, ω is the angular frequency of the external force, and ω0 is the natural frequency of the system.

Plugging in the values, we get:

T = 2π√(2.00 kg / 20.0 N/m) = 1.99 s

To find the angular frequency ω, we can use the formula ω = 2πf, where f is the frequency of the external force. In this case, the frequency is given by the argument of the sine function, which is 2πt. So ω = 2π(2π) = 4π rad/s.

Now, we can plug in the values for ω and ω0 to find the amplitude A:

A = (3.00 N / 2.00 kg) / √((4π)^2 - (2π)^2) = 0.75 m

Therefore, the period of the motion is 1.99 seconds and the amplitude is 0.75 meters. These values are in agreement with the book's answers. It is possible that there was an error in your calculations or the equations used were not appropriate for this problem. It is important to double-check your work and make sure you are using the correct equations for the given situation.