6. BONUS PROBLEM (CALCULUS BASED - NON NUMERICAL PROBLEM). Here we are designated to observe a block placed in an inclined plane. A block of mass M slides down a plane of angle 0. We are interested in determining the (a) speed the block after it has descended through height h, assuming that it starts from rest and that the coefficient of friction u is constant. (b) What is the change in the gravitational potential energy at the initial and final points of the block. (c) Find the work done by the friction. Mind you that on part c you have to evaluate the integral. Hint: Draw a free body diagram and use the energy approach. Answers will be labeled all you have to do is to show the procedure on how we arrived at the results. Answer (a) v = M 2(1- u cot0)gh, (b) AU = mgh, and (c) W = -Mg cos 0 µ(x)dx. {
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.
6. Can you please THOROUGHLY explain how did you solve this? I need it in step by step format because I'm going to explain it in class. Please help me, thank you
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