A particle at the end of a spring executes simple harmonic motion with a period ${t_1}$, while the corresponding period for another spring is ${t_2}$. If the period of oscillation with the two springs in series is $T$, then
A particle at the end of a spring executes simple harmonic motion with a period ${t_1}$, while the corresponding period for another spring is ${t_2}$. If the period of oscillation with the two springs in series is $T$, then
- [AIEEE 2004]
- A
$T = {t_1} + {t_2}$
- B
${T^2} = t_1^2 + t_2^2$
- C
${T^{ - 1}} = t_1^{ - 1} + t_2^{ - 1}$
- D
${T^{ - 2}} = t_1^{ - 2} + t_2^{ - 2}$
Similar Questions
A mass $m$ is attached to two springs of same force constant $K$, as shown in following four arrangements. If $T_1, T_2, T_3$ and $T_4$ respectively be the time periods of oscillation in the following arrangements, in which case time period is maximum?
A mass $m$ is attached to two springs of same force constant $K$, as shown in following four arrangements. If $T_1, T_2, T_3$ and $T_4$ respectively be the time periods of oscillation in the following arrangements, in which case time period is maximum?
In the reported figure, two bodies $A$ and $B$ of masses $200\, {g}$ and $800\, {g}$ are attached with the system of springs. Springs are kept in a stretched position with some extension when the system is released. The horizontal surface is assumed to be frictionless. The angular frequency will be $.....\,{rad} / {s}$ when ${k}=20 \,{N} / {m} .$
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- [JEE MAIN 2021]
A mass $m = 1.0\,kg$ is put on a flat pan attached to a vertical spring fixed on the ground. The mass of the spring and the pan is negligible. When pressed slightly and released, the mass executes simple harmonic motion. The spring constant is $500\,N/m.$ What is the amplitude $A$ of the motion, so that the mass $m$ tends to get detached from the pan ? (Take $g = 10\,m/s^2$ ). The spring is stiff enough so that it does not get distorted during the motion.
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- [JEE MAIN 2013]
What provides the restoring force in the following cases ?
$(1)$ Compressed spring becomes force for oscillation.
$(2)$ Displacement of water in $U\,-$ tube,
$(3)$ Displacement of pendulum bob from mean position.
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$(1)$ Compressed spring becomes force for oscillation.
$(2)$ Displacement of water in $U\,-$ tube,
$(3)$ Displacement of pendulum bob from mean position.
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