What is the formula of time period of spring mass system?

Option 1 : \(T = 2\pi\sqrt{m \over k_1+k_2}\)

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15 Questions 15 Marks 12 Mins

CONCEPT:

Time period (T): The time taken to complete one oscillation is called the time period.

The time period of a spring-mass system is given by:

\(T = 2\pi\sqrt{m \over k}\)

where m is the mass, and k is the spring constant.

The parallel combination of spring: Figure a,b, and c shows the parallel combination of two springs for the spring-mass system.

The effective coefficient of spring in parallel combination is given by

 \(k_{eff} = k_1+k_2+....\)

• The Series combination of spring: The figure shows the series combination of two springs for the spring-mass system.

The effective coefficient of spring in series combination is given by:

\({1\over k_{eff}}={1\over k_{1}}+{1\over k_{2}}+...\)

CALCULATION:

We have to calculate the time period of spring-mass balance for which mass m is connected with two springs k1 and k2 in parallel:

\(T = 2\pi\sqrt{m \over k_{eff}}\)

For the parallel combination of springs k1 and k2

\(k_{eff} = k_1+k_2\)

So \(T = 2\pi\sqrt{m \over k_1+k_2}\)

Hence the correct answer is option 1.

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