A simple pendulum that consists of a small metal ball attached to a long string oscillating with the amplitude of 10 cm and it moves with a speed of 2.5 m/s through the equillibrium position in the positive x-direction. Determine the length of the string.

A 5.00 kg bob is connected to the ceiling via a light string, while an 8.50 kg uniform rod is also connected to the ceiling at one of its ends. Both objects are capable of oscillating in simple harmonic motion and share the same length, which is 2.25 m. Calculate the oscillation period for each pendulum under small displacements? If the mass of the bob is doubled, will there be any change in the period of the oscillations? Moreover, if the mass of the rod is quadrupled, will there be any alteration in the period of the oscillations? To ensure that both pendulums swing with an identical period while maintaining the length of the rod, what should be the new length of the string connected to the bob?

A 0.900 kg block sliding on a horizontal frictionless surface is attached to a horizontal spring with k= 420 N/m. Let x be the displacement of the block from the position at which the spring is unstretched. At t= 0 the block passes through x = 0 with a speed of 4.20 m/s in the positive x direction. What are the (a) frequency and (b) amplitude of the block's motion? (a) Number i Units (b) Number i Units

When dragonflies hover, they tend to “bob” up and down with a motion that is a very good approximation to simpleharmonic motion. Suppose that a dragonfly is at x = A at time t = 0, and that its bobbing motion has an amplitude ofA = 0.40 cm and a period of T = 0.24 s. Find (a) the position, (b) the velocity, and (c) the acceleration of the dragonflyat the time t = 0.10 s.