Determine the period of a car whose mass is 3280 kg and whose shock absorbers ha

Question

Determine the period of a car whose mass is 3280 kg and whose shock absorbers have a spring constant of 6.5 times 10^4 N/m after hitting a bump. Assume the shock absorbers arc poor, so the car really oscillates up and down. 0.14 sec 1.4 sec 3.3 sec 22 see 504 see The cone of a loudspeaker oscillates in SHM at a frequency of 262 Hz ("middle C"). The amplitude at the center of the cone is A = 3 times 10^minus4 m. and at t = 0. x = A. What is the position of the cone at t = 1.00 ms (= 1.00 times 10^minus3 s)? -0.011 mm -0.023 mm 0.15 mm 0.011 mm None of the Above A spring stretches 0.150 m when a 0.300-kg mass is gently attached to it. The spring is then set up horizontally with the 0.300-kg mass resting on a frictionlcss table. The mass is pushed so that the spring is compressed 0.300 m from the equilibrium point, and released from rest. The blocks maximum velocity is: 0.808 m/s 1.61 m/s 2.01 m/s 2.42 m/s None of the Above

Explanation / Answer

10)

period is given by

T = 2*pi*sqrt(m/k)

T = 2*(22/7)*sqrt(3280/(6.5*10^4)) = 1.41 sec

11)

equation of displacement for SHM

x = A*sin(wt)

w = 2*pi*f = 2*(22/7)*262 = 1646.85 rad/s

at t = 1.0 ms

so x = 3*10^(-4)*sin(1646.85*10^(-3)) = 0.3*10^(-3) m

12)

kx = mg

k = mg/x = 0.3*9.8/0.15 = 19.6 N/m

let maximum velocity = v

(1/2)kx^2 = (1/2)mv^2

v = sqrt(kx^2/m) = sqrt(19.6*(0.3)^2/0.3) = 2.42 m/s

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