Physics 101 Lecture 20 Elasticity and Oscillations l

Physics 101: Lecture 20 Elasticity and Oscillations l Today’s lecture will cover Textbook Chapter 10. 5 -10. 10 Physics 101: Lecture 20, Pg 1

Review Energy in SHM l A mass is attached to a spring and set to motion. The maximum displacement is x=A èEnergy = U + K = constant! = ½ k x 2 + ½ m v 2 èAt maximum displacement x=A, v = 0 Energy = ½ k A 2 + 0 èAt zero displacement x = 0 Energy = 0 + ½ mvm 2 ½ k A 2 = ½ m v m 2 vm = (k/m) A èAnalogy with gravity/ball PES x 0 m x=0 Physics 101: Lecture 20, Pg 2 x

Kinetic Energy ACT In Case 1 a mass on a spring oscillates back and forth. In Case 2, the mass is doubled but the spring and the amplitude of the oscillation are the same as in Case 1. In which case is the maximum kinetic energy of the mass bigger? A. Case 1 B. Case 2 C. Same Physics 101: Lecture 20, Pg 3

Potential Energy ACT In Case 1 a mass on a spring oscillates back and forth. In Case 2, the mass is doubled but the spring and the amplitude of the oscillation are the same as in Case 1. In which case is the maximum potential energy of the mass and spring bigger? A. Case 1 B. Case 2 C. Same Physics 101: Lecture 20, Pg 4

Velocity ACT In Case 1 a mass on a spring oscillates back and forth. In Case 2, the mass is doubled but the spring and the amplitude of the oscillation are the same as in Case 1. Which case has the larger maximum velocity? 1. Case 1 2. Case 2 3. Same Physics 101: Lecture 20, Pg 5

Simple Harmonic Motion: Quick Review x(t) = [A]cos( t) v(t) = -[A ]sin( t) a(t) = -[A 2]cos( t) x(t) = [A]sin( t) OR v(t) = [A ]cos( t) a(t) = -[A 2]sin( t) xmax = A Period = T (seconds per cycle) vmax = A Frequency = f = 1/T (cycles per second) amax = A 2 Angular frequency = = 2 f = 2 /T Physics 101: Lecture 20, Pg 6

Natural Period T of a Spring l Simple Harmonic Oscillator è = 2 f = 2 / T èx(t) = [A] cos( t) èv(t) = -[A ] sin( t) èa(t) = -[A 2] cos( t) l Draw FBD write F=ma Physics 101: Lecture 20, Pg 7

Period ACT If the amplitude of the oscillation (same block and same spring) is doubled, how would the period of the oscillation change? (The period is the time it takes to make one complete oscillation) A. The period of the oscillation would double. B. The period of the oscillation would be halved C. The period of the oscillation would stay the same x +2 A t -2 A Physics 101: Lecture 20, Pg 8

Equilibrium position and gravity l If we include gravity, there are two forces acting on mass. With mass, new equilibrium position has spring stretched d Physics 101: Lecture 20, Pg 9

Vertical Spring ACT Two springs with the same k but different equilibrium positions are stretched the same distance d and then released. Which would have the larger maximum kinetic energy? 1) M 2) 2 M 3) Same PE = 1/2 k y 2 Y=0 Physics 101: Lecture 20, Pg 10

Pendulum Motion l For small angles q L T x m mg Physics 101: Lecture 20, Pg 11

Preflight 1 Suppose a grandfather clock (a simple pendulum) runs slow. In order to make it run on time you should: 1. Make the pendulum shorter 2. Make the pendulum longer Physics 101: Lecture 20, Pg 12

Elevator ACT A pendulum is hanging vertically from the ceiling of an elevator. Initially the elevator is at rest and the period of the pendulum is T. Now the pendulum accelerates upward. The period of the pendulum will now be A. greater than T B. equal to T C. less than T Physics 101: Lecture 20, Pg 13

Preflight Imagine you have been kidnapped by space invaders and are being held prisoner in a room with no windows. All you have is a cheap digital wristwatch and a pair of shoes (including shoelaces of known length). Explain how you might figure out whether this room is on the earth or on the moon Physics 101: Lecture 20, Pg 14

Summary l Simple Harmonic Motion èOccurs when have linear restoring force F= -kx èx(t) = [A] cos( t) èv(t) = -[A ] sin( t) èa(t) = -[A 2] cos( t) l Springs èF = -kx èU = ½ k x 2 è = sqrt(k/m) l Pendulum (Small oscillations) è = (g/L) Physics 101: Lecture 20, Pg 15