A conical pendulum is constructed with a string length of 0.475 meters and is set into motion with a radius of 0.180 meters. What is the period of the pendulum's circular motion?
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
Question:
A conical pendulum is constructed with a string length of 0.475 meters and is set into motion with a radius of 0.180 meters. What is the period of the pendulum's circular motion?
My Comments:
I'm using F = m* (v^2 / r) and I am solving for velocity which comes out to approximately 1.33 m/s. Is that what they are looking for and is period the same thing as velocity since it is moving in circular motion? Also, why is the string length given? Am I supposed to be using that information or is it to throw me off? Just curious if I'm missing out on what I need to know.
For the conical pendulum, the time period equation can be derived as below:
T cos θ = mg
T = mg/cosθ..........................(i)
Again, T sinθ = mv2/r
Using the equation (i), we have
mg tanθ = mv2/ r
v = √(rg tanθ)...............................(ii)
Also, we know
v = 2πr / T
From (ii), √(rg tanθ) = 2πr / T
Since, r = lsinθ
T is given by,
T =
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