For assigned homework and Othuh ludlllllly l Problems 11-1 to 11-3 Simple Harmon

Question

For assigned homework and Othuh ludlllllly l Problems 11-1 to 11-3 Simple Harmonic Motion 1. If a particle undergoes sHM with amplitude 0.21 m, what is the total distance it travels in one period? 2. (The springs of a 1700-kg car compress 5.0 mm when its 66 kg driver gets into the driver's seat. If the car goes over a bump, what will be the frequency of oscillations? Ignore damping 3. (M) An elastic cord is 61 cm long when a weight of 75 N hangs from it but is 85 cm long when a weight of 210 N hangs from it. What is the "spring" constant k of this elastic cord? stick if the child has a mass of 32 kg and bounces once every 2.0 seconds. hangs from it. (a) What is the spring stiffness constant and (b) what will be the amplitude and frequency of if the fish is pulled down 2.1 cm more and released so that it oscillates up and down? The web caught in a spider's web stant k for is the value of with a frequency of 4.0 the web the web? the effective spring con- 322 to (b) At what frequency would you expect CHAPTER if an insect of 0.44 were trapped? 11 oscillations and Waves

Explanation / Answer

1)

total distance s = 4*A = 4*0.21 = 0.84 m <<<==ANSWER

2)

spring constant K = mg/x = (66*9.8)/0.005 = 129360 N/m

frequency f = (1/2pi)*sqrt(k/M) = (1/(2pi))*sqrt(129360/1766) = 1.36 Hz

(3)

initial length = L

change in length = L1 - L

F1 = k*x1

F1 = k*(L1-L)

F2 = k*(L2-L)

F2/F1 = (L2-L)/(L1-L)

210/75 = (0.85-L)/(0.61-L)

L = 143/300 m

K = F1/(L1-L)

K = 75/(0.61-143/300)

K = 562.5 N/m

=================

(4)

time period T = 2*pi*sqrt(m/K)

2 = 2*pi*sqrt(32/k)

K = 315.8 N/m

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5)

stiffness =F/x = mg/x = 2.4*9.8/0.036 = 653.33 N/m

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