(13%) Problem 1: One kind of cuckoo clock keeps time by using a mass bouncing on a spring, usually something cute like a cherub in a chair. DA What is the force constant, in newtons per meter, needed to produce a period of 0.25 s for a 0.013-kg mass on the spring? Grade Summary K= Deductions 0% Potential 100% sin() cos() tan() 7 8 HOME Submissions Attempts remaining: 20 cotan() asin() acos() E A 4 5 6 (0% per attempt) atan() acotan() sinh() 2 3 detailed view cosh() tanh() cotanh() 0 END O Degrees O Radians VO BACKSPACE DEL CLEAR Submit Hint Feedback I give up!(13%) Problem 2: A mass is connected to a spring and is allowed to move horizontally. The mass is at a position L when the spring is unstretched. The mass is then moved, stretching the spring, and released from rest. It then moves with simple harmonic motion. L thcexpcrtta.com D a 33% Part (a) At the instant that the mass passes through the position where the spring is unstretched, What can be said about its instantaneous acceleration? It is zero. It is non-zero but not maximum. G'ade Summary . . Deductlons 0% It is maximum. Potential 100% Submit Hint Feedback I give up! Submissions Attempts remaining: Hints: 2% deduction per hint. Hints remaining: 4 Feedback: 2% deduction per feedback. (ipcr attempt) detailed View E 5 33% Part (b) At the instant that the mass passes through the position where the spring is unstretched, what can be said about its instantaneous speed? E A 33 % Part (c) At the instant that the spring is compressed the most, what can be said about the magnitude of its instantaneous velocity? (13%) Problem 3: A spring hangs vertically from a bracket at its unweighted equilibrium length, as shown in the left-most image. An object with mass m is attached to the lower end of the spring, and it is gently lowered until the spring reaches its new equilibrium length, as shown in the center figure. Referring to the right-most figure, the mass is raised until the spring returns to its original length, and then it is released from rest resulting in vertical oscillations. K k m m A 50% Part (a) If the spring constant is 12 N/m, and the mass of the object is 0.35 kg, find the oscillation amplitude, in meters. Grade Summary A = m Deductions 1% Potential 100% sin() cos() tan() JI 7 8 9 HOME Submissions Attempts remaining: 20 cotan() asin() acos() E 4 5 6 (0% per attempt) atan() acotan() sinh() 2 3 detailed view cosh() tanh() cotanh() + 0 END Degrees O Radians VO BACKSPACE DEL CLEAR Submit Hint Feedback I give up! Hints: 2% deduction per hint. Hints remaining: 2 Feedback: 2% deduction per feedback. 4 50% Part (b) Find the maximum velocity, in meters per second, of the oscillating mass.(13%) Problem 4: A mass m = 3.45 kg is at the end of a horizontal spring on a frictionless horizontal surface. The mass is oscillating with an amplitude A = 1.5 cm and a frequency f = 1.45 Hz. D A 20% Part (a) Write an equation for the spring constant k. Grade Summary k = | Deductions 0% Potential 100% Submissions Attempts remaining: E (0 % per attempt) dEiled view HOME: Move the cursor to the first position. \\ Hints: 2% deduction per hint, Hints remaining: 3 Feedback: 2% deductionper feedback, E A 20% Part (b) Calculate the spring constant k, in Newtons per meter. E A 20% Part (c) Write an equation for the total mechanical energy, E, of the motion. Your expression should be in terms of the variables in the original problem statement. E A 20% Part (d) Calculate the total mechanical energy E , in joules. E A 20% Part (e) If the amplitude is doubled, what happens to the total mechanical energy? Choose the best answer (13%) Problem 5: A simple pendulum, consisting of a mass on a string of length L, is undergoing small oscillations with amplitude A. D a 25 % Part (a) The mass is increased by a factor of four. What is true about the period? Choose the best answer. The period doubles. 333:\":uunslmary 0'7 ' 0 The period decreases by a factor of four. potential 100% The period is halved. The period remains unchanged. Subunssnons ' _ Th . d . b f t f f Attempts remaining: i e perio Increases y a ac or 0 our. (% per attempt) detailed view Submit Hint Feedback I give up! Hints: 2% deduction per hint. Hints remaining: 1 Feedback: 2% deduction per feedback. & 25% Part (b) The length is increased by a factor of four. What is true about the period? Choose the best answer. 5 25% Part (c) The amplitude is doubled. What is true about the period? Choose the best answer. 3 25% Part (d) The pendulum is taken to the Moon. Which of the following is true about the period? Choose the best answer. (13%) Problem 6: While visiting the Albert Michelson exhibit at Clark University, you notice that a chandelier (which looks remarkably like a simple pendulum) swings back and forth in the breeze once every T = 6.9 seconds. Randomized Variables T = 6.9 seconds [> B 25% Part (a) Calculate the frequency of oscillation (in Hertz) of the chandelier. Grade Summary f = I Deductions 0% Potential 100% cos() tan() J1: ( ) 7 8 9 HOME Submissions . Attempts remaining: E asm() acos() E 1'A AJ, 4 5 6 *- (% per attempt) acotanO sinh() / * 1 2 3 - \"ended \"aw tanh() cotanhO + - 0 . END ODegrees Radians J0 BACKSPACE DH. CLEAR Submit | Hint | Feedback | I give up! Hints: 2% deduction per hint. Hinm remaining: 3 Feedback: 2% deduction per feedback. & 25 % Part (b) Calculate the angular frequency a) of the chandelier in radians/second. E 3 25% Part (c) Determine the length L in meters of the chandelier. A 25 % Part ((1) That evening, while hanging out in J .J . Thompson's House 0' Blues, you notice that (coincidentally) there is a chandelier identical in every way to the one at the Michelson exhibit except this one swings back and forth 0.11 seconds slower, so the period is T + 0.11 seconds. Determine the acceleration due to gravity in In/s2 at the club. (13%) Problem 8: A novelty clock has a 0.0095 kg mass object bouncing on a spring which has a force constant of 1.35 N/m. D A 50% Part (a) What is the maximum velocity of the object, in meters per second, if the object bounces 2.45 cm above and below its equilibxium position? Grade Summary Vmax = I Deductions 0% Potential 100% sin() cos() tan() :1: ( 7 8 9 SAubmissions 20 . ttempts remaining: cotan() asm() acos() E 4 5 6 (% per attempt) atan() acotanO sinh() 1 3 detailed view Hints: 2% deduction per hint, Hints remaining: 1 Feedback: 2% deduction per feedback. E A 50% Part (b) How much kinetic energy, in joules, does the object have at its maximum velocity