1. Physics 1D03 - Lecture 331 Harmonic Motion ( II ) (Serway 15.2, 15.3) Mass and Spring Energy in SHM

2. Physics 1D03 - Lecture 332 Velocity and Acceleration a(t)  2 x(t)

3. Physics 1D03 - Lecture 333 Energy in SHM M Look again at the block & spring We could also write E = K+U = ½ m(v max ) 2

4. Physics 1D03 - Lecture 334 Question: Suppose U=½ kA 2 at t = 0, and T=1 sec. When is U=K during the cycle? (i.e. when do their curves cross?)

5. Physics 1D03 - Lecture 335 U, K oscillate back and forth “out of phase” with each other; the total E is constant. U K E t T

6. Physics 1D03 - Lecture 336 Armed with the equation of motion: and the expressions for energy: We can solve a large range of problems in SHM. Example 1: A 0.25kg block is oscillating on a spring with k=4N/m. At t=0, v=-0.2m/s and a=+0.5m/s 2. Find its total energy and the equation of motion.

7. Physics 1D03 - Lecture 337 Solution

8. Physics 1D03 - Lecture 338 Example 2: A 50.0g object connected to a spring k=35.0N/m oscillates on a horizontal, frictionless surface with an amplitude of 4.0cm. Find: a) the total energy of the system b) the speed of the object when the position is 1.0cm c) the kinetic energy when x=3.0cm d) the potential energy when x=3.0cm.

9. Physics 1D03 - Lecture 339 Example 3: A 200 g mass is attached to a horizontal spring and executes SHM with a period of 0.25s. The total energy of the system is 2.0J. a) Find the force constant of the spring b) Find the amplitude of the motion

10. Physics 1D03 - Lecture 3310 Example 4: A car having a mass of 1000kg is driven into a brick wall. The car’s bumper behaves like a spring of constant 5x10 6 N/m and compresses 3.16 cm as the car is brought to rest. What was the speed of the car before impact, assuming no mechanical energy loss with the wall?

11. Physics 1D03 - Lecture 3311 Example 5: A particle executes SHM with an amplitude of 3.0 cm. At what position does its speed equal one half of its maximum speed?

12. Physics 1D03 - Lecture 3312 Example 6: A uniform disc is connected to a spring and allowed to roll back and forth without slipping. What is the angular frequency of the oscillations?