A simple harmonic oscillator takes 13.5 s to undergo six complete vibrations. (a) Find the period of its motion. s (b) Find the frequency in hertz. Hz (c) Find the angular frequency in radians per second. rad/s Need Help? Read It Watch It

Is it possible to have damped oscillations when a system is at resonance? Explain.

We do not need the analogy in Equation 16.30 to write expressions for the translational displacement of a pendulum bob along the circular arc s(t), translational speed v(t), and translational acceleration a(t). Show that they are given by s(t) = smax cos (smpt + ) v(t) = vmax sin (smpt + ) a(t) = amax cos(smpt + ) respectively, where smax = max with being the length of the pendulum, vmax = smax smp, and amax = smax smp2.

Give an example of a simple harmonic oscillator, specifically noting how its frequency is independent of amplitude.

Some people modify cars to be much closer to the ground than when manufactured. Should they install stiffer springs? Explain your answer.

Check Your Understanding Identify one way you could decrease the maximum velocity of a simple harmonic oscillator.

The angular position of a pendulum is represented by the equation = 0.032 0 cos t, where is in radians and = 4.43 rad/s. Determine the period and length of the pendulum.

. A mass of 0.75 kg is attached to a relaxed spring with k = 2.5 N/m. The mass rests on a horizontal, frictionless surface. If the mass is displaced by 0.33 m, what is the magnitude of the force exerted on the mass by spring? If the mass is then released to execute simple harmonic along the surface, with what frequency will it oscillate?

If a car has a suspension system with a force constant of 5.00104 N/m , how much energy must the car’s shocks remove to dampen an oscillation starting with a maximum displacement of 0.0750 m?

If the speed of the observer is increased by 5.0%, what is the period of the pendulum when measured by this observer?