Simple Harmonic Motion - 5 Steps to a 5 500 AP Physics Questions to Know by Test Day

5 Steps to a 5 500 AP Physics Questions to Know by Test Day (2012)

Chapter 9. Simple Harmonic Motion

241. A mass (M) is on a frictionless incline of θ radians and is attached to a spring with spring constant, K. When the mass is pulled down the slope, what will be its period of oscillation when released?

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242. A 1-m-long narrow rod is fixed to the ceiling. It has a torsional spring constant of C and a rigid rod of length R. The negligible mass is attached perpendicularly to the narrow rod’s end. On the end of the rigid rod is a small mass, M. If the mass and rod are twisted through θ radians, at what period will the mass and rod torsionally oscillate?

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(C)T =20.07cps

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243. A mass is attached to a spring, which is attached to a pivot on the ceiling. The period of the spring’s oscillation is equal to the period of the pendulum’s oscillation. Assuming no friction in the system, what happens to the mass when it is moved to one side and released?

(A) The mass moves up and down.

(B) The mass swings from side to side.

(C) The mass swings from side to side and moves up and down.

(D) The mass swings from side to side and then moves up and down, and the motions repeat.

(E) The mass moves up and down and then swings side to side, and the motions repeat.

244. The Moon is approximately 384,000 km from the Earth. The Moon revolves around the Earth once every 27.3 days. What is the frequency of the Moon’s motion?

(A) 14,065 km/d

(B) 0.037 rpd

(C) 0.0366300366… rpd

(D) 0.037 rph

(E) 27.3 days

245. A bell is hung in Notre Dame’s north tower. The bell and its clapper swing with the same period. When Quasimodo tries to ring the bell, it does not sound. Why?

(A) He is not pulling the bell rope hard enough.

(B) The bell and clapper move as one body.

(C) Because they have the same period, the bell and clapper move as one body.

(D) Quasimodo is deaf.

(E) The clapper cannot reach the bell.

246. In Question 245, how can Quasimodo make the bell ring using a clapper?

(A) Use a clapper with a smaller mass on the end so it is out of period with the bell.

(B) Use a clapper with a bigger mass on the end so it is out of period with the bell.

(C) Use a shorter clapper so it is out of period with the bell.

(D) Use a longer clapper so it is out of period with the bell.

(E) Use a longer clapper with a larger mass on the end.

247. Why does putting your legs under the seat of a swing at the bottom of its motion, then outwardly swinging your legs at the top of the motion increase the height of the swing’s motion?

(A) The kick at the top of the swing adds energy to the system.

(B) Putting your legs under the swing raises your center of gravity.

(C) The kinetic energy of swinging your legs adds to the energy of the swing.

(D) Raising your legs raises your center of gravity.

(E) Raising your legs adds potential energy to the swing, and kicking them adds kinetic energy.

248. What is special about a Foucault pendulum?

(A) Foucault invented it.

(B) It can be used as a clock.

(C) It moves in one plane and the Earth moves under it.

(D) It is the only demonstration that the Earth rotates.

(E) It is very big.

249. A meter stick is held at one end by a frictionless pivot and is held horizontally at the other end. Neglecting air resistance, how far will the meter stick swing when released?

(A) It will swing around the pivot and back to the starting point.

(B) It will swing just short of horizontal on the other side of the pivot.

(C) It will swing just beyond horizontal on the other side of the pivot.

(D) It will swing to horizontal on the other side of the pivot.

(E) It will drop to vertical.

250. A common office toy consists of five steel balls, each suspended by two strings and each touching the adjacent ball(s). When a ball at the end is raised and then dropped, it hits the adjacent ball and the ball at the other end rises. Why?

(A) The energy in the system must be conserved.

(B) The potential energy of the center balls keeps them in place.

(C) The kinetic energy of the moving ball is transferred through the set of balls, when it hits them, to the only ball that can move, causing it to rise.

(D) The potential energy of the moving ball is transferred through the set of balls to the only ball that can move, causing it to rise.

(E) The center balls are glued together and do not move.

251. Why will a pendulum not oscillate in zero gravity?

(A) The pendulum has no weight in zero gravity.

(B) A pendulum requires gravity as well as the pendulum’s mass to create the restoring force.

(C) There is no up or down in zero gravity.

(D) The pendulum would be too far from the Earth to work in zero gravity.

(E) The pendulum requires gravity to work.

252. Will a pendulum swing in an accelerating space ship? What would be its period?

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(B) No

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253. If a ball tied to a string is swung around in a horizontal circle, is it moving periodically?

(A) Yes

(B) No

(C) Yes, but only if it moves like a sine wave

(D) Yes, but only if it moves like a cosine wave

(E) Yes, but only if it makes a harmonic sound

254. If the string on the swing ball above is released, what will be the ball’s trajectory?

(A) It will continue to move in a circle.

(B) It will curve away from the center point.

(C) It will move in a straight line.

(D) It will move in a straight line tangential to where it was released.

(E) It will move in a straight line tangential to where it was released and curve downward.

255. Some large oil tankers have an antiroll water tank inside the hull that matches the resonant frequency of the ship’s hull. So, when ocean waves hit the ship at the resonant frequency, how does the water tank prevent the ship from capsizing in the waves?

(A) The energy of the waves is used by the water in the tank.

(B) The waves enter the tank and are dampened.

(C) The water tank is 180° out of phase with the ship’s hull.

(D) The water tank is 90° out of phase with the ship’s hull.

(E) The water in the tank is in phase with the ship’s hull.

256. A pendulum has a bob of 28 kg and is 38 cm in diameter. It is hung on a wire that is 67 m long. What is its period and frequency?

(A) 0.06 s and 16.43 cycles/s

(B) 16.43 s and 0.06 cycles/s

(C) 0.608689441 s and 16.42873907 cycles/s

(D) 10.62 s and 0.09 cycles/s

(E) 0.09 s and 10.62 cycles/s

257. A mass of 50 kg is held vertically by a spring on each end of the mass. Both springs have a spring constant of 20 N/m. When set in motion, what is the system’s period?

(A) 14.04962946 s

(B) 7.024814731 s

(C) 14.05 s

(D) 7.02 s

(E) 0.14 s

258. A mass of 50 kg is held vertically by two springs, one connected to the other. Each spring has a spring constant of 20 N/m. When set in motion, what is the system’s period?

(A) 0.14 s

(B) 14.05 s

(C) 7.02 s

(D) 14.04962946 s

(E) 7.024814731 s

259. A mass of 50 kg is held horizontally on a frictionless surface by two springs, one at each end of the mass. Each spring has a spring constant of 20 N/m. When set in motion, what is the system’s period?

(A) 14.04962946 s

(B) 7.024814731 s

(C) 14.05 s

(D) 7.02 s

(E) 0.14 s

260. A mass of 50 kg is held horizontally on a frictionless surface by two springs, one connected to the other. Each spring has a spring constant of 20 N/m. When set in motion, what is the system’s period?

(A) 0.14 s

(B) 14.05 s

(C) 7.02 s

(D) 14.04962946 s

(E) 7.024814731 s

261. A 10-kg mass is placed on a frictionless surface and attached to a spring that is attached to a fixed wall. The spring’s constant is 20 N/m. When set in motion, what is the system’s period? What is the period if the system is held vertically?

(A) 4.4 s and 8.9 s

(B) 8.885765876 s for both

(C) 8.885765876 s and 17.77153175 s

(D) 4.4 s for both

(E) 12.6 s for both

262. A 15-kg mass rests on two springs and is held by a spring attached to the ceiling. The spring constant for each of the bottom two springs is 10 N/m; for the upper spring 25, it is N/m. When set in motion, what is the system’s period?

(A) 3.6 s

(B) 7.2 s

(C) 1.8 s

(D) 1.2 s

(E) The mass will not move

263. A mass of 12 kg is hung onto a spring attached to the ceiling. The spring’s constant is 19 N/m. How far will the spring stretch when the weight is hung, and what will be the system’s period when activated?

(A) 6.2 cm and 15 s

(B) 6.2 m and 5 min

(C) 62 mm and 5 s

(D) 6.2 m and 15.6 s

(E) 6.2 m and 156 s

264. A refrigerator compressor that weighs 8 kg is fixed to three springs on the refrigerator frame. Each has a spring constant of 0.01 N/m. What is the natural frequency of the system?

(A) 0.10 cycles/s

(B) 0.03 cycles/s

(C) 0.8 cycles/s

(D) 1.2 cycles/s

(E) 0.003 cycles/s

265. The pendulum on an old mechanical, weight-driven clock has a period of 3 s. What is the length of the clock’s pendulum?

(A) 8 cm

(B) 71 mm

(C) 0.08 s

(D) 0.71 m

(E) 0.08 m

266. A blue light wave vibrates at 6.662 ×10−11 Hz. What is its wavelength?

(A) 4,900 × 10−10 m

(B) 4,500 × 10−10 m

(C) 4,200 × 10−10 m

(D) 4,500 × 1010 m

(E) 4,500 × 10−10 m

267. A steel ball with a mass of 100 g is dropped onto a steel plate. The collision is perfectly elastic. From what height must the ball be dropped for the vibrating system to have a period of 2 s?

(A) 100 cm

(B) 19.6 m

(C) 0.1 m

(D) 9.8 m

(E) 4.9 m

268. A pendulum consists of a rigid rod that is 8 cm long with a 100-g mass on one end and a frictionless pivot attached to a plate on the other end. What must be done to the plate when the system is inverted (i.e., mass on the top, plate on bottom) to keep the pendulum oscillating?

(A) Nothing, the pendulum will fall over when it is inverted.

(B) Oscillate the plate side to side opposite the pendulum’s swing to keep it upright.

(C) Oscillate the plate vertically in time with the pendulum.

(D) Oscillate the plate vertically with acceleration greater than gravity.

(E) Oscillate the plate vertically at the pendulum’s frequency.

269. Consider a homogeneous sphere with a diameter of 12,800 km (approximately the size of the Earth). The sphere has a smooth, straight, frictionless hole bored through the diameter. Neglecting air resistance, will a ball dropped into the hole experience periodic motion? And, if so, what is its period?

270. A spring/mass system is vibrating according to 20 cos ωt. The mass is 10 kg, and the spring constant is 5 cm/N. The amplitude constant is 20 cm. Determine the frequency, period, and maximum and minimum amplitudes of the system.