PhysicsBowl 2018 Q39

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PhysicsBowl 2018

39) This question requires some basic knowledge on simple harmonic motion. We are given a sinusoidal equation in terms of t and asked to find the period.

Where y is position, A is amplitude, ω is angular frequency, t is time, and θ is the phase shift

Whenever we deal with simple harmonic motion, the position of the object can be expressed either of these forms. Just like translational motion, we can take the first derivative to find the velocity, or the second derivative to find the acceleration.

It is important to take notice that these equations only work for simple harmonic motion. If there are any external forces(like friction or air resistance), we will have a damped oscillation.

This question asks us to find the period of the function. Using ω, we can set up an expression for period.

Where ω is angular frequency, T is period, and f is frequency

If we compare the equation given in the problem, to the general equation, we can find ω(angular frequency) and solve for T(period).

Where y is position, A is amplitude, ω is angular frequency, t is time, θ is the phase shift, and T is period

Answer: D