Use MATLAB to solve the problem and give the code also.

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Harmonic Motions of Similar Models. The unifying power of mathematical methods results to a large extent from the fact that different physical (or other) systems may have the same or very similar models. Illustrate this for the following three systems (a) Pendulum clock: A clock has a 1-meter pendulum. The clock ticks once for each time the pendulum completes a full swing, returning to its original position. How many times a minute does the clock tick? (b) Flat spring: The harmonic oscillations of a flat spring with a body attached at one end and horizontally clamped at the other are also governed by (3). Find its motions, assuming that the body weighs 8 nt (about 1.8 lb), the system has its static equilibrium 1 cm below the horizontal line, and we let it start from this position with initial velocity 10 cm/sec. Fig. Flat Spring (c) Torsional vibrations: Undamped torsional vibrations (rotations back and forth) of a wheel attached to an elastic thin rod or wire are governed by the equation, where is the angle measured from the state of equilibrium. Solve this equation for initial angle and initial angular velocity 20 sec. 1 (=0.349 rad # sec). I Harmonic Motions of Similar Models. The unifying power of mathematical methods results to a large extent from the fact that different physical (or other) systems may have the same or very similar models. Illustrate this for the following three systems (a) Pendulum clock: A clock has a 1-meter pendulum. The clock ticks once for each time the pendulum completes a full swing, returning to its original position. How many times a minute does the clock tick? (b) Flat spring: The harmonic oscillations of a flat spring with a body attached at one end and horizontally clamped at the other are also governed by (3). Find its motions, assuming that the body weighs 8 nt (about 1.8 lb), the system has its static equilibrium 1 cm below the horizontal line, and we let it start from this position with initial velocity 10 cm/sec. Fig. Flat Spring (c) Torsional vibrations: Undamped torsional vibrations (rotations back and forth) of a wheel attached to an elastic thin rod or wire are governed by the equation, where is the angle measured from the state of equilibrium. Solve this equation for initial angle and initial angular velocity 20 sec. 1 (=0.349 rad # sec)