You visited us 2 times! Enjoying our articles? Unlock Full Access!

Damped Oscillations

Two springs, ...

Question

Two springs, of force constant $k_{1}$ and $k_{2}$ , are connected to a mass m as shown. The frequency of oscillation of the mass is $f$ . If both $k_{1}$ and $k_{2}$ are made four times their original values, the frequency of oscillation becomes

f / 2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

f / 4

No worries! We‘ve got your back. Try BYJU‘S free classes today!

4 f

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2 f

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $2 f$
This system can be treated as two parallel spring system with spring constants $k_{1}$ and $k_{2}$ . Now, frequency
$f = \frac{1}{2 π} \sqrt{\frac{k_{1} + k_{2}}{m}}$
When both $k_{1}$ and $k_{2}$ are made four times their original value, the new frequency becomes:
$f^{'} = \frac{1}{2 π} \sqrt{\frac{4 k_{1} + 4 k_{2}}{m}}$
$= \frac{1}{2 π} 2 \sqrt{\frac{k_{1} + k_{2}}{m}}$
$= 2 f$

Suggest Corrections

Similar questions

Two springs of force constants $K_{1}$ and $K_{2}$ are connected to a mass m as shown. The frequency of oscillation of the mass is f. If both $K_{1}$ and $K_{2}$ are made four times their original values, the frequency of oscillation becomes:

Q. Two springs of force constants

k_{1}

and

K_{2}

are connected to a mass m as shown in figure (a) and (b). what is the ratio of the time periods of vertical oscillation in cases (a) and (b) if

k_{1} = k_{2}

Q. Two springs of force constants

k_{1}

and

k_{2}

are connected as shown figure. The time period of vertical oscillations of mass m is given by

Q. When mass

m

oscillates with spring of spring constant

k_{1}

its frequency is

3 H z

and with spring of spring constant

k_{2}

its frequency is

6 H z

. Then frequency of oscillations when mass is connected with spring as shown in figure is:-

Q. Two springs of force constants

K_{1}

and

K_{2}

are connected to a mass m placed on a horizontal frictionless surface as shown in figure. (a) and (b). what is the ratio of the time periods of horizontal oscillation in cases (a) and (b) if

K_{1} = K_{2}

Join BYJU'S Learning Program

Two springs, of force constant k1 and k2, are connected to a mass m as shown. The frequency of oscillation of the mass is f. If both k1 and k2 are made four times their original values, the frequency of oscillation becomes

The correct option is D 2fThis system can be treated as two parallel spring system with spring constants k1 and k2. Now, frequencyf=12π√k1+k2mWhen both k1 and k2 are made four times their original value, the new frequency becomes: f′=12π√4k1+4k2m=12π2√k1+k2m=2f

Two springs, of force constant $k_{1}$ and $k_{2}$ , are connected to a mass m as shown. The frequency of oscillation of the mass is $f$ . If both $k_{1}$ and $k_{2}$ are made four times their original values, the frequency of oscillation becomes