Question

How can resonance frequency be reduced?

Answer 1

Hint: Recall the condition at which resonance occurs and the equation of resonant frequency. From the equation itself it is possible to answer this question. You also have to remember the definition of resonant frequency.

Complete answer:
Resonance is the phenomenon in which amplitude is increased when the frequency of an applied periodic force matches with the natural frequency of the system. To increase the sound and in signal transmission this condition is used. Resonant frequency will be equal to natural frequency.

We have the equation for natural frequency as
$f=\frac{1}{2\pi }\sqrt{\frac{k}{m}}$
where k is the force constant. It is also called stiffness.
m is mass.

For a two particle system reduced mass is used. From the equation we can say that to change the resonant frequency stiffness or mass should be altered. As resonant frequency is same as the natural frequency, if we increase the natural frequency consequently resonant frequency also increases.

So resonant frequency can be reduced by the following ways:
1. If mass is increased, then we can reduce the natural frequency and it is possible to reduce the peak value by increasing damping. But this will lower the response and widens the range of response.
2. Stiffening raises the natural frequency thereby reducing the resonance frequency. It should be done without adding mass. Reducing the forcing function can also reduce the range of response.

Note: Remember that resonant frequency and natural frequency are the same, not different. Only when frequency becomes equal to natural frequency then resonance happens. So, when natural frequency increases resonant frequency also increases and vice-versa.