SHM Hr Physics Chapter 11 Notes Simple Harmonic

SHM Hr Physics Chapter 11 Notes

Simple Harmonic Motion Objectives Identify the conditions of simple harmonic motion. n Explain how force, velocity, and acceleration change as an object vibrates with simple harmonic motion. n Calculate the spring force using Hooke’s law. n

Simple Harmonic Motion n Simple Harmonic Motion gives a regular repeating action. ¨ Any periodic motion that is the result of a restoring force that is proportional to displacement. n Springs, Masses, Pendula, and Bells, exhibit a periodic motion, therefore, SHM.

Hooke's Law n Hooke's Law says that the restoring force due to a spring is proportional to the length that the spring is stretched, and acts in the opposite direction. If we imagine that there are no other forces, and let x represent the distance the spring is stretched at time t then the restoring force might be represented as -kx where k is the spring constant and k > 0.

Hooke’s Law Concept Check n If a mass of 0. 55 kg attached to a vertical spring stretches the spring 36 cm from its original equilibrium position, what is the spring constant?

Hooke’s Law Concept Check n 15 N/m

Hooke’s Law Concept Check n A load of 45 N attached to a spring is hanging vertically stretches the spring 0. 14 m. What is the spring constant?

Hooke’s Law Concept Check n 3. 2 x 102 N/m

Hooke’s Law Concept Check n A slingshot consists of a light leather cup attached between two rubber bands. If it takes a force of 32 N to stretch the bands 1. 2 cm, what is the equivalent spring constant of the two rubber bands?

Hooke’s Law Concept Check n 2. 7 x 103 N/m

Hooke’s Law Concept Check n How much force is required to pull a spring 3. 0 cm from its equilibrium position if the spring constant is 2. 7 x 103 N/m?

Hooke’s Law Concept Check n 81 N

The Simple Pendulum The restoring force is a component of the bob’s weight, so F= Fg sin θ n For small angles (less than 1 ), the motion of a pendulum approximates simple harmonic motion. n

Measuring Simple Harmonic Motion Objectives Identify the amplitude of vibration n Recognize the relationship between period and frequency n Calculate the period and frequency of an object vibrating with simple harmonic motion n

Galileo’s Laws of the Pendulum Concept Check n You need to know the height of a tower, but darkness obscures the ceiling. You note that a pendulum extending from the ceiling almost touches the floor and has a period of 24 s. How tall is the tower?

Concept Check n 1. 4 x 102 m

Concept Check n You are designing a pendulum clock to have a period of 1. 0 s. How long should the pendulum be?

Concept Check n 25 cm

Concept Check n A trapeze artist swings in simple harmonic motion with a period of 3. 8 s. Calculate the length of the cable supporting the trapeze.

Concept Check n 3. 6 m

Concept Check n Calculate the period and frequency of a 3. 500 m long pendulum at the following locations: ¨ The North Pole, where g=9. 832 m/s 2 ¨ Chicago, where g = 9. 802 m/s 2 ¨ Jakarta, Indonesia, where g=9. 782 m/s 2

Concept Check 3. 749 s; 0. 2667 Hz n 3. 754 s; 0. 2664 Hz n 3. 758 s; 0. 2661 Hz n

Simple Harmonic Motion of a Mass. Spring System n The period of a mass-spring system depends on the mass and the spring constant. n T= 2 (m/k)