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AP Physics Monday 14.02.03 Standards: 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 1. Warm Up 2. Wavelike Motion 3. Simple Harmonic Motion: Springs Warm Up What is the spring constant of a spring that is stretched 2cm by a 50g mass? Homework C#8 AP Physics Tuesday 14.02.04 Standards: 3b,c apply the expression for the period of a simple pendulum. Objective: SWBAT solve simple pendulum problems. Agenda 1. Warm Up 2. Review HW 3. Simple Pendulum Notes 4. C#9 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 Homework C#9 AP Physics Wednesday 14.02.12 Standards: analyze problems for vertical and horizontal oscillations of springs Objective: SWBAT solve complex problems involving simple harmonic motion Agenda 1. Warm Up 2. Review HW 3. Energy in Simple Harmonic Motion. 4. Guided Practice FRQ 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 Homework Begin 4 page SHM extension worksheet AP Physics Thursday 14.02.06 Standards: analyze problems for vertical and horizontal oscillations of springs Objective: SWBAT solve complex problems involving simple harmonic motion 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? Agenda 1. Pass out Warm Up Found in the black box. (students know where it is) 2. Give Warm Up 7 min. 3. Give students answer xequilibrium=4.9m, U=24J 4. Collect Warm up and put it in black box. 5. Hand out Oscillations Extension Worksheet. Students will work the rest of the period. Homework Oscillation Extension HW Packet AP Physics Friday 14.02.10 Standards: analyze problems for vertical and horizontal oscillations of springs Objective: SWBAT solve complex problems involving simple harmonic motion Agenda 1. Pass out Warm Up Found in the black box. (students know where it is) 2. Give Warm Up 8 min. 3. Give students answer Δxextension=5.9m, Δxcompress=3.9m 4. Collect Warm up and put it in black box. 5. Hand out Oscillations Extension Worksheet. Students will work the rest of the period. 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. Homework Oscillations Extension Worksheet 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 A m p l i t u d e w=√(k/m) is the angular frequency or angular velocity of oscillating mass. y=Acos(wt) y (m) T=2π√(m/k) for a spring T=2π√(l/g) for a pendulum time (s) T Frequency: The number of oscillations per second or f=1/T C#8 Simple Harmonic Motion Springs a. T=20s f=? b. T=? f=80Hz c. T=? k=40 N/m m=15kg d. T=? F=20 N x=4m k=? m=15kg w=? f=? 1. (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? 2. (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? 3. (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? 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 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 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. (1) An earthworm found in Africa was 6.7 m long. If this worm were a simple pendulum, what would its period be? 2. (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? 3. (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. 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