What is the natural frequency of the spring mass system shown below? The contact between the block and the inclined plane is frictionless. The mass of the block is denoted by m and the spring constants are denoted by k_{1} and k_{2} as shown below.

- \(\sqrt {\frac{{{k_1} + {k_2}}}{{2m}}}\)
- \(\sqrt {\frac{{{k_1} + {k_2}}}{{4m}}}\)
- \(\sqrt {\frac{{{k_1} - {k_2}}}{m}}\)
- \(\sqrt {\frac{{{k_1} + {k_2}}}{2m}}\)
- \(\sqrt {\frac{{{k_1} + {k_2}}}{m}}\)

Option 5 : \(\sqrt {\frac{{{k_1} + {k_2}}}{m}}\)

Free

ST 1: Reasoning & Mental Ability

7404

15 Questions
15 Marks
15 Mins

**Concept:**

Let the mass is displaced x downwards in the direction of the wedge.

Spring force F_{1} = k_{1}x and F_{2} = k_{2}x acts in the direction opposite to the direction of displacement force.

Net force, F = (k1 + k2)x

As the system is in equilibrium

mẍ + F = 0

⇒ mẍ + (K_{1} + K_{2})x = 0

⇒ mẍ \( + \left( {\frac{{{k_1} + {k_2}}}{m}} \right)x = 0\)

\(\therefore {\omega _n} = \sqrt {\frac{{{k_1} + {k_2}}}{m}} \)

India’s **#1 Learning** Platform

Start Complete Exam Preparation

Daily Live MasterClasses

Practice Question Bank

Mock Tests & Quizzes

Trusted by 2,28,89,225+ Students

Start your FREE coaching now >>

Testbook Edu Solutions Pvt. Ltd.

1st & 2nd Floor, Zion Building,

Plot No. 273, Sector 10, Kharghar,

Navi Mumbai - 410210

[email protected]
Plot No. 273, Sector 10, Kharghar,

Navi Mumbai - 410210

Toll Free:1800 833 0800

Office Hours: 10 AM to 7 PM (all 7 days)