CONCEPTUAL QUESTIONS (Damped Harmonic Motion)1. Give an example of a damped harmonic oscillator. (They are more common than undamped orsimple harmonic oscillators.)2. How would a car bounce after a bump under each of these conditions?(a) overdamping(b) underdamping(c) Critical damping3. Most harmonic oscillators are damped and, if undriven, eventually come to a stop. Why?CONCEPTUAL QUESTIONS (Driven Harmonic Motion and Resonance)4. Why are soldiers in general ordered to “route step" (walk out of step) across a bridge?5. Do you think there is any harmonic motion in the physical world that is not damped harmonicmotion? Try to make a list of five examples of undamped harmonic motion and dampedharmonic motion. Which list was easier to make?6. Some engineers use sound to diagnose performance problems with car engines. Occasionally,a part of the engine is designed that resonates at the frequency of the engine. The unwantedoscillations can cause noise that irritates the driver or could lead to the part failing prematurely.In one case, a part was located that had a length L made of a material with a mass M. What canbe done to correct this problem?

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5. A mass of 25 g moves with simple harmonic motion. It has "springiness" of 1.5 N/m and friction causes it to slow down with a damping constant of 250 g/s. Is the system overdamped or underdamped? What would the damping constant need to be for the system to be critically damped?
2. Solve the motion of the damped harmonic oscillator driven by a force Fext(t) = Fo cos² wt
6. A 2.0 kg mass attached to a 24.0 N/m massless spring is driven by an external force F = F, cos (2nt) where Fo= 12.0 N. Assuming that the damping coefficient b is so small that it can be neglected, find a) the period of the oscillator, and b) the amplitude of its motion.
10. A mass-spring system moves with simple harmonic motion along the x axis between turning points at x, = 20 cm and x= 60 cm. For parts (i) through (iii), choose from the same five possibilities. (i) At which position does the particle have the greatest magnitude of momentum? (a) 20 cm (b) 30 cm (c) 40 cm (d) some other position (e) The greatest value occurs at multiple points. (ii) At which position does the particle have greatest kinetic energy? (iii) At which position does the particle-spring system have the greatest total energy?
5. An object is attached to a spring and completes only one cycle (i.e. goes back and forth and stops). The object reaches its maximum velocity after 0.250 seconds of motion. Calculate the its angular frequency and the spring constant if the object is 0.125 kg.
3. Below given figure shows a simple oscillator with damping. In this, a mass m is attached to a spring (spring constant k) and a damper with damping force proportional to -bv. The spring and the damper are attached to the walls on the opposite sides of the mass (see Figure). The oscillator can be driven either by moving an attachment point on the damper (Case I) or the end of the spring (Case II). In both cases, the position of the attachment point as a function of time is s(t) = so cos(wat). For BOTH of the above cases, answer each of the following questions. (i). Write the equations of motion of the mass m. (ii). Find the amplitude of steady state solution in terms of given parameters. P Figure: Two weays dn've an oiilator Cae I: mwwo m to Sct) cale II!

1. Give an example of a damped harmonic oscillator. (They are more common than undamped or simple harmonic oscillators.)