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

  • Option 1)

    2f

  • Option 2)

    f/2

  • Option 3)

    f/4

  • Option 4)

    4f

 

Answers (1)

As we learnt in

Parallel combination of spring -

- wherein

K_{eq}=K_{1}+K_{2}

K_{1}and\ K_{2} are spring constants of spring 1 & 2 respectively.

 

 

 

In the given figure two springs are connected in parallel. Therefore the effective spring constan is given by

k_{eff}= k_{1}+k_{2}                

Frequency of oscillation,

f= \frac{1}{2\pi }\sqrt{\frac{k_{eff}}{m}}= \frac{1}{2\pi }\sqrt{\frac{k_{1}+k_{2}}{m}}\cdots \cdots \cdots \cdots (i)

As    k_{1}   and   k_{1}   are increased four times N ew frequency,

{f}'= \frac{1}{2\pi }\sqrt{\frac{4\left ( k_{1}+k_{2} \right )}{m}}= 2f\: \: \: (Using (i))

Correct option is 1.


Option 1)

2f

This is the correct option.

Option 2)

f/2

This is an incorrect option.

Option 3)

f/4

This is an incorrect option.

Option 4)

4f

This is an incorrect option.

Preparation Products

Knockout JEE Main April 2021 (One Month)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 14000/- ₹ 4999/-
Buy Now
Knockout JEE Main May 2021

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 22999/- ₹ 9999/-
Buy Now
Test Series JEE Main May 2021

Unlimited Chapter Wise Tests, Unlimited Subject Wise Tests, Unlimited Full Mock Tests, Get Personalized Performance Analysis Report,.

₹ 6999/- ₹ 2999/-
Buy Now
Knockout JEE Main May 2022

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 34999/- ₹ 14999/-
Buy Now
JEE Main Rank Booster 2021

Booster and Kadha Video Lectures, Unlimited Full Mock Test, Adaptive Time Table, 24x7 Doubt Chat Support,.

₹ 13999/- ₹ 6999/-
Buy Now
Boost your Preparation for JEE Main 2021 with Personlized Coaching