Question

In a spring mass damper system excited by a harmonic force with a damping of 10%. The amplitude at resonance is found to be 10 cm. What will be the amplitude at half the resonance frequency?

• A. 9.81 cm
• B. 4.9 cm
• C. 7.35 cm
• D. 2.64 cm

Answer 1

The correct option is D 2.64 cm

$\xi =0.1,A=10\text{cm (At resonance )}$

$A=\frac{\frac{F_0}{S}}{\sqrt{(1-r^2)+(2\xi r{)}^2}}$

$\text{At resonance ,}r=1=\frac{\omega }{{\omega }_n}$

$\frac{\frac{F_0}{S}}{=}0.1$

$\frac{F_0}{S}=0.02$

$\text{When,}\omega =\frac{{\omega }_n}{2}$

$A^{\prime }=\frac{0.02}{\sqrt{(1-{0.5}^2)+(2\times 0.5\times 0.1{)}^2}}$

$A^{\prime }=0.0264\text{m}=2.64\text{cm}$