A mass $m$ is suspended separately by two different springs of spring constant $K_1$ and $K_2$ gives the time-period ${t_1}$ and ${t_2}$ respectively. If same mass $m$ is connected by both springs as shown in figure then time-period $t$ is given by the relation
A$t = {t_1} + {t_2}$
B$t = \frac{{{t_1}.{t_2}}}{{{t_1} + {t_2}}}$
C${t^2} = {t_1}^2 + {t_2}^2$
D${t^{ - 2}} = {t_1}^{ - 2} + {t_2}^{ - 2}$
AIPMT 2002, Medium
Download our app for free and get started
D${t^{ - 2}} = {t_1}^{ - 2} + {t_2}^{ - 2}$
d (d) ${t_1} = 2\pi \sqrt {\frac{m}{{{K_1}}}} $ and ${t_2} = 2\pi \sqrt {\frac{m}{{{K_2}}}} $
Equivalent spring constant for shown combination is
$K_1 + K_2$. So time period $t$ is given by $t = 2\pi \sqrt {\frac{m}{{{K_1} + {K_2}}}} $
By solving these equations we get ${t^{ - 2}} = t_1^{ - 2} + t_2^{ - 2}$
Download our app
and get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
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.
A particle executes linear simple harmonic motion with an amplitude of $2\, cm$. When the particle is at $1\, cm$ from the mean position the magnitude of its velocity is equal to that of its acceleration. Then its time period in seconds is
A spring is stretched by $5 \,\mathrm{~cm}$ by a force $10 \,\mathrm{~N}$. The time period of the oscillations when a mass of $2 \,\mathrm{~kg}$ is suspended by it is :(in $s$)
A uniform cylinder of length $L$ and mass $M$ having cross-sectional area $A$ is suspended, with its length vertical, from a fixed point by a massless spring, such that it is half submerged in a liquid of density $\sigma $ at equilibrium position. When the cylinder is given a downward push and released, it starts oscillating vertically with a small amplitude. The time period $T$ of the oscillations of the cylinder will be