1. A 6.50-kg object is hung from the bottom end of a vertical spring fastened to an overhead beam. The object is set into vertical oscillations having a period of 2.30 s. Find the force constant of the spring. 2. A 65.0-g object connected to a spring with a force constant of 40.0 N/m oscillates with an amplitude of 8.00 cm on a frictionless, horizontal surface. (a) Find the total energy of the system. mJ (b) Find the speed of the object when its position is 1.20 cm. (Let 0 cm be the position of equilibrium.) m/s (c) Find the kinetic energy when its position is 3.00 cm. mJ (d) Find the potential energy when its position is 3.00 cm. mJ 3. A physical pendulum in the form of a planar object moves in simple harmonic motion with a frequency of 0.500 Hz. The pendulum has a mass of 2.00 kg, and the pivot is located 0.400 m from the center of mass. Determine the moment of inertia of the pendulum about the pivot point. 4. A pendulum with a length of 1.00 m is released from an initial angle of 14.5°. After 1 000 s, its amplitude has been reduced by friction to 3.50°. What is the value of b/2m?
Added by Tamara B.
Step 1
30 s and the mass of the object is 6.50 kg, we can use the formula for the period of a mass-spring system: \( T = 2\pi \sqrt{\frac{m}{k}} \), where T is the period, m is the mass, and k is the force constant of the spring. Show more…
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