A mass $M$ is suspended from a light spring. An additional mass m added displaces the spring further by a distance $x$. Now the combined mass will oscillate on the spring with period
$T = 2\pi \sqrt {\left( {mg/x(M + m)} \right)} $
$T = 2\pi \sqrt {\left( {(M + m)x/mg} \right)} $
$T = (\pi /2)\sqrt {\left( {mg/x(M + m)} \right)} $
$T = 2\pi \sqrt {\left( {(M + m)/mgx} \right)} $
The time period of a mass suspended from a spring is $T$. If the spring is cut into four equal parts and the same mass is suspended from one of the parts, then the new time period will be
If a body of mass $0.98\, kg$ is made to oscillate on a spring of force constant $4.84\, N/m$, the angular frequency of the body is ..... $ rad/s$
Assuming all pulleys, springs and string massless. Consider all surface smooth. Choose the correct statement $(s)$
The frequency of oscillation of a mass $m$ suspended by a spring is $v_1$. If length of spring is cut to one third then the same mass oscillates with frequency $v_2$, then
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.