Warm Up What is the spring constant of a spring that is stretched 2cm by a 50g mass?

1. Warm Up What is the spring constant of a spring that is stretched 2cm by a 50g mass? AP PhysicsMonday 14.02.03Standards: apply the expression for period of oscillation to the mass of a spring.Objective: SWBAT find the period of SHM applied to horizontal springs Agenda • Warm Up • Wavelike Motion • Simple Harmonic Motion: Springs Homework C#8

2. AP PhysicsTuesday 14.02.04Standards: 3b,c apply the expression for the period of a simple pendulum. Objective: SWBAT solve simple pendulum problems. Warm Up The period of a spring-mass system undergoing simple harmonic motion is T. If the amplitude of the spring-mass system’s motion is doubled, the period will be: a)1/4T b) ½ T c) T d) 2T e) 4T Agenda • Warm Up • Review HW • Simple Pendulum Notes • C#9 Homework C#9

3. AP PhysicsWednesday 14.02.12 Standards: analyze problems for vertical and horizontal oscillations of springsObjective: SWBAT solve complex problems involving simple harmonic motion Warm Up Find the length of a simple pendulum on earth consisting of a light string swinging at 20° to the vertical with a 8 kg bowling ball suspended from the end of the string if the period is 3 minutes Agenda • Warm Up • Review HW • Energy in Simple Harmonic Motion. • Guided Practice FRQ Homework Begin 4 page SHM extension worksheet

4. Warm Up A spring with a spring constant of 2N/m is attached to the ceiling of the classroom. Hanging from the spring is a 1 kg mass. How far will the spring’s new equilibrium position be from its original position. How much energy is stored in the spring at this position? AP PhysicsThursday 14.02.06Standards: analyze problems for vertical and horizontal oscillations of springsObjective: SWBAT solve complex problems involving simple harmonic motion Agenda • Pass out Warm Up Found in the black box. (students know where it is) • Give Warm Up 7 min. • Give students answer xequilibrium=4.9m, U=24J • Collect Warm up and put it in black box. • Hand out Oscillations Extension Worksheet. Students will work the rest of the period. Homework Oscillation Extension HW Packet

5. Warm Up The 2 N/m spring with the 1 kg mass hanging from it from yesterday engages in simple harmonic motion when 20 J of work is done on it in the downward direction to give the motion an amplitude of 1 m. a) What is the maximum compression and extension of the spring from its unstretched position. Hint: The natural unstretched position refers to the spring’s equilibrium position with no effects of gravity. AP PhysicsFriday 14.02.10Standards: analyze problems for vertical and horizontal oscillations of springsObjective: SWBAT solve complex problems involving simple harmonic motion Agenda • Pass out Warm Up Found in the black box. (students know where it is) • Give Warm Up 8 min. • Give students answer Δxextension=5.9m, Δxcompress=3.9m • Collect Warm up and put it in black box. • Hand out Oscillations Extension Worksheet. Students will work the rest of the period. Homework Oscillations Extension Worksheet

6. Profile of Wavelike Motion Amplitude-is the magnitude of the wave or how high or intense the wave gets. For springs and pendulum this is the height of the wave w=√(k/m) is the angular frequency or angular velocity of oscillating mass. Amplitude y=Acos(wt) y (m) time (s) T Frequency: The number of oscillations per second or f=1/T T=2π√(m/k) for a spring T=2π√(l/g) for a pendulum

7. C#8 Simple Harmonic Motion Springs d. T=? F=20 N x=4m k=? m=15kg w=? f=? c. T=? k=40 N/m m=15kg a. T=20s f=? b. T=? f=80Hz • (1) A hummingbird makes a humming sound with its wings, which beat with a frequency of 90.0 Hz. Suppose a mass is attached to a spring with a spring constant of 2.50x102N/m. How large is the mass if its oscillation frequency is 3.00x10-2 times that of a hummingbird’s wings? • (3) A double coconut can grow for 10 years and have a mass of 20.0 kg. If a 20.0 kg double coconut oscillates on a spring 42.7 times each minute, which is the spring constant of the spring? • (5) Suppose a 2662 kg giant seal is placed on a scale and produces a 20.0 cm compression. If the seal and spring system are set into simple harmonic motion, what is the period of the oscillations?

8. Guided Practice A large pearl was found in the Phillipines in 1934. Suppose the pearl is placed on a spring scale whose spring constant is 362 N/m If the scale’s platform oscillates with a frequency of 1.20 Hz, what is the mass of the pearl? m=6.37 kg

9. Simple Pendulum Guided Practice Two friends in France use a pendulum hanging from the world’s highest railroad bridge to exchange messages across a river. One friend attaches a letter to the end of the pendulum and releases it so that the pendulum swings across the river to the other friend. the bridge is 130.0 m above the river. How much time is needed for the letter to make one swing across the river? Assume the river is 16.0 m wide. t=11.4 s

10. C#9 Simple Harmonic Motion of a Simple Pendulum a. Givens T=? l=2m g=9.8m/s2 b. Givens T=20 min l=? g=9.8m/s2 c. Givens T=200s l=12m g=? • (1) An earthworm found in Africa was 6.7 m long. If this worm were a simple pendulum, what would its period be? • (3) If bamboo, which can grow 88 cm in a day, is grown for four days and used to make a simple pendulum, what will be the pendulum’s period? • (6) Ganymede, the largest of Jupiter’s moons, is also the largst satellite in the solar system. Find the acceleration of gravity on Ganymede if a simple pendulum with a length of 1.00 m has a period of 10.5 s.

11. Guided Practice • 1983B2. A block of mass M is resting on a horizontal, frictionless table and is attached as shown above to a relaxed spring of spring constant k. A second block of mass 2M and initial speed vo collides with and sticks to the first block Develop expressions for the following quantities in terms of M, k, and vo • a. v, the speed of the blocks immediately after impact • b. x, the maximum distance the spring is compressed • c. T, the period of the subsequent simple harmonic motion