Numerical - Damped natural frequency, given disturbing force & ξ

Q.  Calculate damped natural frequency, if a spring mass damper system is subjected to periodic disturbing force of 30 N. Damping coefficient is equal to 0.76 times of critical damping coefficient and undamped natural frequency is  5 rad/sec
- Published on 11 Sep 15

a. 3.99 rad/sec
b. 2.13 rad/sec
c. 4.12 rad/sec
d. 3.24 rad/sec

ANSWER: 3.24 rad/sec

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    Discussion

  • Vasanth Roy   -Posted on 06 Nov 20
    F = 30 N
    c = 0.76 cc
    wn = 5 rad/s
    wd = root(wn^2 - (c/2m)^2)
    wd = root(wn^2 - (0.76cc/2m)^2)
    wd = root(5^2 - (0.76 * 2m * wn/2m)^2)
    wd = root(25 - (.76*5)^2)
    wd = root(25 - (.76*5)^2)
    wd = 3.249 rad/s

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