STARTER The period of a pendulum depends on: a.The mass. b.The string length. c.The release angle. d.All of these. The period of a pendulum depends on: a.The mass. b.The string length. c.The release angle. d.All of these.

Simple Harmonic Motion Masses & Springs 2.03 Simple harmonic motion (SHM) occurs when the acceleration and the displacement are related by: a = -Cx where C is a constant.

Mass/Spring System F = -kx ( Hooke’s Law) But F = ma so a = (-k/m)x SHM

The Displacement for SHM

Example

The Pendulum

Pendulum Example A student wants to make a pendulum with a mass and a string that has a period of 1.00 second. How long should the string be?

Energy in SHM Mass/Spring System: KE = (1/2)mv 2 PE = (1/2)kx 2 E total = (1/2)kx 2 max = KE + PE v = 0 : PE = E = (1/2)kx 2 max x = 0 : KE = E = (1/2)mv 2 max

Example A.500kg mass on a spring ( k = 400N/m ) is pulled back.25m and released from rest. Find: 1.The maximum velocity. 2.The total energy. 3.The maximum force on the mass. 4.The period of the motion. A.500kg mass on a spring ( k = 400N/m ) is pulled back.25m and released from rest. Find: 1.The maximum velocity. 2.The total energy. 3.The maximum force on the mass. 4.The period of the motion. 2. E = (1/2)kx 2 max = (1/2)(400)(.25 2 ) = 12.5J 3. F max = kx max = 400(.25) = 100N