A ‘‘seconds pendulum’’ beats seconds; that is, it takes 1 s for half a cycle in 4cm distance. (a) What is the length of a simple ‘‘seconds pendulum’’ at a place where g = 9.8 m/s2 ? (b) Determine its angular frequency? & (c) Calculate its speed at the equilibrium position?

Answer the following questions based in Pendulum Experiment: At what point is the PE the greatest? At what point is the KE the greatest? Describe how the two bars (KE and PE) are related to each other and how these relationships change as the pendulum moves through its cycle.

a) Use energy conservation to find the amplitude of the motion. b) Use energy conservation to find the maximum speed of the glider.   c) What is the angular frequency of the oscillations?      (express in rad/s)

CL ANO A pendulum with a length of 1.00 m is released from an initial angle of 14.0°. After 1 000 s, its amplitude has been reduced by friction to 6.50°. What is the value of b/2m? Need Help? Watch It

Grandfather clocks are designed so they can be adjusted by moving the weight at the bottom of the pendulum up or down. Suppose you have a grandfather clock at home that runs slow by 6 seconds per minute, or 10%. Which of the following adjustment(s) would make it more accurate? (This is a multi-select question. You may select one or more options.) O Decrease the amplitude of swing by 10%. Decrease the length of the pendulum to approximately (0.9)2 times the original length. Take away mass from the weight because the period is inversely proportional to square root of the mass. Increase the length of the pendulum to approximately (1.1)2 times the original length. Add more mass to the weight because the period is proportional to square root of the mass. Increase the amplitude of swing by 10%.

A 2.0-kg ball executing a simple harmonic motion has the following velocity as a function of time: v=-A w sin w t, where A= 1.0 m and @ = 20 rad/s. At what time (first time after the ball started) will the kinetic energy of the ball be 100 J?

The potential energy of an object attached to a spring is 2.50 J at a location where the kinetic energy is 1.40 J. If the amplitude ? of the simple harmonic motion is 22.0 cm, calculate the spring constant ? and the magnitude of the largest force ?spring, max that the object experiences.

A simple pendulum with a length of 1.73 m and a mass of 6.74 kg is given an initial speed of 2.36 m/s at its equilibrium position. (a) Assuming it undergoes simple harmonic motion, determine its period (in s). (b) Determine its total energy (in J). (c) Determine its maximum angular displacement (in degrees). (For large v, and/or small /, the small angle approximation may not be good enough here.) (d) What If? Based on your answer to part (c), by what factor would the total energy of the pendulum have to be reduced for its motion to be described as simple harmonic motion using the small angle approximation where 0 ≤ 10°?

The potential energy of an object attached to a spring is 2.60 J at a location where the kinetic energy is 1.30 J. If the amplitude ?of the simple harmonic motion is 19.0 cm, calculate the spring constant ? and the magnitude of the largest force ?spring, max that the object experiences.

The device pictured in the following figure entertains infants while keeping them from wandering. The child bounces in a harness suspended from a door frame by a spring. (a) If the spring stretches 0.250 m while supporting an 8.0-kg child, what is its force constant? (b) What is the time for one complete bounce of this child? (c) What is the child’s maximum velocity if the amplitude of her bounce is 0.200 m?