1 (m+ M)V2 (m+ M)gh (6.8) Here, h is the height of the combined (pendulum bob metal ball) above their lowest point. This relation permits us to calculate the maximum height h that the pendulum reaches from the combined velocity V , which was calculated from the initial velocity of the projectile in the first part Due to the design of our pendulum, we have one final step. We will not be measuring the height h which the cup in the pendulum rises to, but rather the angle 0 through which it sweeps. By examining figure 1, it is clear that h can be represented function of 0 in the following way: as a R(cos 00 - cos 0) (6.9) h 11
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.
FInd the full derivation of the two equations below solving the expression for the velocity of the metal ball in terms of the angle θ swept through by the pendulum.
1/2 (m+M)V^2 = (m+M)gh
h = R(cos θ0 − cos θ)
Picture of the equations are attached.
Using the values below find the intial velcity using the equation found above. (Answer is 8.16 m/s)
| θ | R | m | M |
| 25 | 30cm | 30g | 300g |
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