SHM Worksheet 2AP Physics CKernion
1. A block of unknown mass is attached to a spring with a spring constant of 6.5 N/m and undergoes SHM with an amplitude of 10.0 cm. When the block is halfway between its equilibrium and endpoint, its speed is measured to be 30.0 cm/s. Calculate the mass of the block, the period of the motion and the maximum acceleration of the block.
2. A 50.0 g object connected to a spring (k= 35.0 N/m) oscillates on a horizontal frictionless surface with an amplitude of 4.00 cm. Find the total energy of the system, the speed when x=1.0 cm, the kinetic and potential energies when x=3.0 cm.
3. A physical pendulum (in the form of a planar body) moves in SHM with a frequency of 0.450 Hz. If the pendulum has a mass of 2.20 kg and the pivot point is located 0.35 m from the CM of the body, determine the rotational inertia of the body.
4. A 10.6 kg object oscillates at the end of a vertical spring whose k= 2.04 x 104 N/m. The effect of air resistance and internal resistance (which makes the spring warm up) is represented by a damping coefficient of b=3.00 Ns/m. Calculate the frequency of the damped oscillation and find the time interval which elapses while the energy of the system drops to 5% of its original value.
5. Assume that you are examining the characteristics of a suspension system of a 2000 kg car. The suspension sags 10 cm when the weight of the car is placed on it. In addition, the amplitude of the oscillation decreases by 50% during one complete oscillation. Estimate the values of k and b for the suspension system of EACH wheel. Assume that each wheel supports 25% of the total mass.
Answers:
1. m=0.542 kg T=1.81 sec amax = 1.20 m/s2
2. E=28.0 mJ speed = 1.02 m/s when x=1.0 cm K=12.2 mJ and U=15.8 mJ at x=3.0 cm
3. I = 0.944 kg m2
4. f = 7 Hz t = 10.6 seconds
5. k=490 N/cm b=1100 kg/s