Table 3: Period of Oscillation for Spring 2 t-Time for 10 complete Period Squared Mass (g) Period (s) T=t/10 oscillations (s) 50g 4.18 0.418 100g 5.85 0.585 250g 9.28 0.928

(a) What is the effect on the period of a pendulum if you double its length? (b) What is the effect on the period of a pendulum if you decrease its length by 5.00%?

Parcels of air (small volumes of air) in a stable atmosphere (where the temperature increases with height) can oscillate up and down, due to the restoring force provided by the buoyancy of the air parcel. The frequency of the oscillations are a measure of the stability of the atmosphere. Assuming that the acceleration of an air parcel can be modeled as 2zt2=g(z)0zz , prove that z=z0etN2 is a solution, where N is known as the Brunt-Väisälä frequency. Note that in a stable atmosphere, the density decreases with height and parcel oscillates up and down.

A spring has a length of 0.200 m when a 0.300kg mass hangs from it, and a length of 0.750 m when a 1.95-kg mass hangs from it. (a) What is the force constant of the spring? (b) What is The unloaded length of the spring?

Explain why you expect an object made of a stiff material to vibrate at a higher frequency than a similar object made of a spongy material.

A 2.00-kg block lies at rest on a frictionless table. A spring, with a spring constant of 100 N/m is attached to the wall and to the block. A second block of 0.50 kg is placed on top of the first block. The 2.00-kg block is gently pulled to a position x=+A and released from rest. There is a coefficient of friction of 0.45 between the two blocks. (a) What is the period of the oscillations? (b) What is the largest amplitude of motion that will allow the blocks to oscillate without the 0.50-kg block sliding off?

A cars 30.0-kg front tire is suspended by a spring with spring constant k = 1.00 105 N/m. At what speed is the car moving if washboard bumps on the road every 0.750 m drive the tire into a resonant oscillation?

The energy of a ripple on a pond is proportional to the amplitude squared. If the amplitude of the ripple is 0.1 cm at a distance from the source of 6.00 meters, what was the amplitude at a distance of 2.00 meters from the source?

An object of mass m is hung from a spring and set into oscillation. The period of the oscillation is measured and recorded as T. The object of mass m is removed and replaced with an object of mass 2m. When this object is set into oscillation, what is the period of the motion? (a) 2T (b) 2T (c) T (d) T/2 (e) T/2

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