Question

A body mass 600 gm is attached to the spring of spring constant k -100 N/m and it is performing damped oscillations if damping constant is 0.2 and driving force isF=F0 where F0=20N.Find the amplitude of oscillaton at resonance.​

Answer 1

A body mass 600 gm is attached to the spring of spring constant k -100 N/m and it is performing damped oscillations if damping constant is 0.2 and driving force isF=F0 where F0=20N. The amplitude of oscillaton at resonance is 7.74 m.​

As we know that the amplitude of forced oscillation is given as

$A = \frac{F_o}{\sqrt{m^2(\omega^2 - \omega_d^2)^2+ \omega_d^2b^2}}$

here we know that when oscillator is in resonance then

$\omega = \omega_d$

so we have

$A = \frac{F_o}{\omega_db}$

$F_0 = 20 N$

m = 600 g

$\omega = \sqrt{\frac{k}{m}}$

$\omega = \sqrt{\frac{100}{0.6}}$

$\omega = 12.9 rad/s$

now we have

$A = \frac{20}{12.9 \times 0.2}$

$A = 7.74 cm$

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Topic : Amplitude to forced oscillations

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