Question

A body of mass $\text{600 gm}$ is attached to a spring of spring constant $\text{k = 100 N/m}$ and it is performing damped oscillations. If damping constant is $0.2$ and driving force is $F=F_0$ $cos\left(\omega t\right)$ where $F_0=20N$ Find the amplitude of oscillation at resonance.

• A. $\text{4.1 m}$
• B. $\text{0.57 m}$
• C. $\text{7.7 m}$
• D. $\text{0.98 m}$

Answer 1

The correct option is C $\text{7.7 m}$

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

$A=\frac{F_0}{\sqrt{m^2({\omega }^2-{\omega }_d^2{)}^2+{\omega }_d^2{b}^2}}$

Here we know that when oscillator is in resonance then,

$\omega ={\omega }_d$

so we have

$A=\frac{F_0}{{\omega }_{d}b}$

$F_0=20N$

$m=600g$

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

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

$\omega =12.9rad/sec$

Now we have

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

$A=7.7m$