A ball of mass m kept at the centre of a string of length `L` is pulled from centre in perpendicular direction and released. Prove that motion of ball is simple harmonic and determine time period of oscillation
Text Solution
Verified by Experts
Restoring force `F = -2Tsintheta` When `theta` is small `sintheta ~~ tantheta ~~ theta = (x)/(L//2)` `m(d^(2)x)/(dt^(2))= - 2Tsintheta = -2Ttheta = -2T(x)/(L//2)` `(d^(2)x)/(dt^(2)) = (4T)/(mL) xx rArr (d^(2)x)/(dt^(2)) prop -x` So motion is simple harmonic `omega = (2pi)/(T) = sqrt((4T)/(mL))rArr T = 2pisqrt((mL)/(4T))`
Topper's Solved these Questions
SIMPLE HARMONIC MOTION
ALLEN |Exercise SOME WORKED OUT EXAMPLES|29 Videos
Two identical springs of spring constant k are attached to a block of mass m and to fixed supports as shown in Fig. 14.14. Show that when the mass is displaced from its equilibrium position on either side, it executes a simple harmonic motion. Find the period of oscillations.
A mass M is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes simple harmonic oscillation with a time period T. If the mass is increased by m, the time period becomes ((5)/(4)T) . The ratio of (m)/(M) is...........
Total charge - Q is uniformly spread along length of a ring of radius R. A small test charge +q of mass m is kept at the centre of the ring and is given a gentle push along the axis of the ring. (a) Show that the particle executes a simple harmonic oscillation. (b) Obtain its time period.
The maximum velocity of a particle executing simple harmonic motion with an amplitude 7 mm is 4.4 m/s. The period of oscillation is.
Find the time period of mass M when displaced from its equilibrium position and then released for the system shown in figure. .
A weightless rigid rod with a load at the end is hinged at point A to the wall so that it can rotate in all directions (Fig). The rod is kept in the horizontal position by a vertical inextensible thread of length 1, fixed at its midpoint. The load receives a momentum in the direction perpendicular to the plane of the figure. Determine the period T of small oscillations of the system.
A ball of mass (m) 0.5 kg is attached to the end of a string having length (L) 0.5 m . The ball is rotated on a horizontal circular path about vertical axis. The maximum tension that the string can bear is 324 N . The maximum possible value of angular velocity of ball ( radian//s) is - .
Two metallic balls of mass m are suspended by two strings of length L . The distance between upper ends is l . The angle at which the string will be inclined with vertical due to attraction is (m lt lt M where M is the mass of Earth)
A body of mass m is attached to the lower end of a spring whose upper end is fixed. The spring has negligible mass when the mass m is slightly pulled down and released, it oscillates with a time period of 3s. When the mass m is increased by 1 kg, the time period of oscillations becomes 5s. The value of m in kg is...........
_S01_029_S01.png)
