The period of oscillation of mass M, hanging from spring of force constant k is T. When additional mass m is attached to spring the period of oscillation becomes 5T/4. m/M=?

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The period of oscillation of mass M, hanging from spring of force constant k is T. When additional mass m is attached to spring the period of oscillation becomes 5T/4. m/M=?

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The period of oscillation of mass M, hanging from spring of force cons...

Given:
- Period of oscillation with mass M: T
- Period of oscillation with mass M + m: 5T/4

Calculating the period of oscillation:
- The period of oscillation of a mass-spring system is given by the formula: T = 2π√(m/k), where m is the mass attached to the spring and k is the force constant of the spring.

Calculating period with mass M:
- Using the formula, for mass M: T = 2π√(M/k)

Calculating period with mass M + m:
- When m is added to mass M, the new period becomes 5T/4: 5T/4 = 2π√((M + m)/k)

Equating the two period equations:
- Equating the two period equations, we get: 2π√(M/k) = 2π√((M + m)/k)
- Simplifying the equation: √(M/k) = √((M + m)/k)
- Squaring both sides: M/k = (M + m)/k
- Solving for m: M = M + m
- Therefore, m/M = 1

Conclusion:
- The ratio of the additional mass m to the original mass M is 1.

Community Answer

The period of oscillation of mass M, hanging from spring of force cons...

T=2π√[m/k] use this formula...

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The period of oscillation of mass M, hanging from spring of force constant k is T. When additional mass m is attached to spring the period of oscillation becomes 5T/4. m/M=?

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