1- A 1.94-kg object oscillates on a spring that has a force constant equal to 41

Question

1- A 1.94-kg object oscillates on a spring that has a force constant equal to 416 N/m. The linear damping constant has a value of b = 1.92 kg/s. The system is driven by a sinusoidal force of maximum value 9.1 N and angular frequency = 10.2 rad/s.

(a) What is the amplitude of the oscillations?
....... cm

(b) If the driving frequency is varied, at what frequency will resonance occur?
....... rad/s

(c) What is the amplitude of oscillation at resonance?
......... cm

(d) What is the width of the resonance curve ?
......... rad/s

-----------------

2-

Two damped, driven spring-mass oscillating systems have identical masses, driving forces, and damping constants. However, system A's force constant kA is four times system B's force constant kB. Assume they are both very weakly damped. How do their resonant frequencies compare?

... A = B

... A = 2B  

.. A = 1/2B

... A = 1/4B

... Their resonant frequencies cannot be compared, given the information provided.

Explanation / Answer

a)

here by using the formula

w0 = sqrt( k / m)

w0 = sqrt(416 / 1.94)

w0 = 14.64 rad/sec

then

A = 10.2 / sqrt(4 * ( 194 - 91)^2 + 4 * 91)

A = 0.05 m = 5 cm

b)

resonance is at w = w0

w resonance = 14.64 rad/sec

c)

here

Areso = 10.2 / sqrt(4 * 194) = 0.36 m = 36 cm

d)

delta w = b / m

delta w = 1.92 / 1.94 = 0.98 rad/sec

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