A metal block with a mass of 4.00 kg oscillates at the end of a vertical spring with a spring constant of 2.80 x 10 N/m. The motion is damped by air resistance, and the damping coefficient is b = 3.00 N - s/m. (a) What is the frequency (in Hz) of the damped oscillation? 13.3 Hz (b) By what percentage does the amplitude of the oscillation decrease in each cycle? 2.8 % (c) Over what time interval (in s) does the energy of the system drop to 5.00% of its initial value? 3.99 S

The motion of a body is described by the equation 1.65 sin (0.470πt) where t is in s and y is in m. (a) Find the amplitude.(b) Find the period.(c) Find the frequency.(d) Find the displacement at t = 3.50 s.(e) Find the displacement at t = 23.0 s.

A 10.6 kg object oscillates at the end of a vertical spring that has a spring constant of 2.05×10^4 N/m. The effect of air resistance is represented by the damping coefficient b = 3.00 kg/s. Calculate the frequency of the damped oscillation.

A pendulum is formed by pivoting a long thin rod about a point on the rod. In a series of experiments, the period is measured as a function of the distance d between the pivot point and the rod's center. (a) If the rod's length is L = 1.11 m and its mass is m = 26.8 g, what is the minimum period? (b) If d is chosen to minimize the period and then L is increased, does the period increase, decrease, or remain the same? (c) If, instead, m is increased without L increasing, does the period increase, decrease, or remain the same?