2. A mass is suspended vertically from a spring so it is at rest at the equilibr

Question

2. A mass is suspended vertically from a spring so it is at rest at the equilibrium point. The mass is pulled straight down to an extension "x and released so that it oscillates about the equilibrium point. The acceleration is greatest in magnitude and directed downward when: A) The mass is somewhere between the equilibrium point and maximum extensiorn. B) The mass is at its maximum upward travel. C) The mass is at the equilibrium point D) The mass is at its maximum lower travel. 3. A pendulum is composed of a 50 cm long thin solid rod with a mass of 300 grams suspended at one end as shown. What is the period of small oscillations about the equilibrium point? A) 1.159 s 8) 0.465 s 0.970 s D) 0 637 s 300 g 4. The velocity of a certain simple harmonic oscillator is given by v-(12 m/s) sin [(6.0 rad/s) ft What is the amplitude of the simple harmonic motion? A) 6.0 m B) 8.0 m C) 2.0 m D) 4.0 m 1410 3B-Pagel

Explanation / Answer

13.

wf = wi + alpha*t

wf = 0 + 2*3 = 6 rad/sec

tangential velocity = V = w*r

V = 6*3 = 18 cm/sec

14.

KErot = 0.5*I*w^2

I = moment of inertia of cylinder = M*r^2

w = V/r

KErot = 0.5*(M*r^2)*(V/r)^2 = 0.5*M*V^2

KErot = 0.5*20*5^2 = 250 J

15.

linear displacement is given by:

s = r*theta

r = 4 m

theta = 30 deg = pi/6

s = 4*pi/6 = 2.09 m

16.

x = 12*sin wt

max acceleration is given by:

a = A*w^2

A = amplitude = 12 cm

w = sqrt (k/m) = sqrt (6/2) = (sqrt 3) rad/sec

a = 12*3 = 36 cm/sec^2

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