The average speed of the bob of a simple pendulum oscillating with a small amplitude $A$ and time period $T$ is
AIIMS 2009, Medium
Download our appand 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.*
Similar Questions
- 1A particle is performing simple harmonic motionView Solution
$(i)$ its velocity-displacement graph is parabolic in nature
$(ii)$ its velocity-time graph is sinusoidal in nature
$(iii)$ its velocity-acceleration graph is elliptical in nature
Correct answer is - 2Phase space diagrams are useful tools in analyzing all kinds of dynamical problems. They are especially useful in studying the changes in motion as initial position and momentum are changed. Here we consider some simple dynamical systems in one-dimension. For such systems, phase space is a plane in which position is plotted along horizontal axis and momentum is plotted along vertical axis. The phase space diagram is $x(t)$ vs. $p(t)$ curve in this plane. The arrow on the curve indicates the time flow. For example, the phase space diagram for a particle moving with constant velocity is a straight line as shown in the figure. We use the sign convention in which position or momentum upwards (or to right) is positive and downwards (or to left) is negative. $Image$View Solution
$1.$ The phase space diagram for a ball thrown vertically up from ground is
mcq $Image$
$2.$ The phase space diagram for simple harmonic motion is a circle centered at the origin. In the figure, the two circles represent the same oscillator but for different initial conditions, and $E_1$ and $E_2$ are the total mechanical energies respectively. Then $Image$
$(A)$ $ E_1=\sqrt{2} E_2$ $(B)$ $ E_1=2 E_2$
$(C)$ $ E_1=4 E_2$ $(D)$ $ E_1=16 E_2$
$3.$ Consider the spring-mass system, with the mass submerged in water, as shown in the figure. The phase space diagram for one cycle of this system is $Image$
mcq $Image$
Give the answer question $1,2$ and $3.$
- 3Four massless springs whose force constants are $2k, 2k, k$ and $2k$ respectively are attached to a mass $M$ kept on a frictionless plane (as shown in figure). If the mass $M$ is displaced in the horizontal direction, then the frequency of oscillation of the system isView Solution
- 4A body is vibrating in simple harmonic motion with an amplitude of $0.06\, m$ and frequency of $15\, Hz$. The velocity and acceleration of body isView Solution
- 5A body is executing $S.H.M.$ When its displacement from the mean position is $4\, cm$ and $5\, cm$, the corresponding velocity of the body is $10 \,cm/sec$ and $8\, cm/sec$. Then the time period of the body isView Solution
- 6View SolutionFor the system given below, find the angular frequency of oscillation ?
- 7$Assertion :$ For a particle performing $SHM$, its speed decreases as it goes away from the mean position.View Solution
$Reason :$ In $SHM$, the acceleration is always opposite to the velocity of the particle. - 8In the given figure, a body of mass $M$ is held between two massless springs, on a smooth inclined plane. The free ends of the springs are attached to firm supports. If each spring has spring constant $k,$ the frequency of oscillation of given body is :View Solution
- 9If the maximum velocity and maximum acceleration of a particle executing $SHM$ are equal in magnitude, the time period will be .... $\sec$View Solution
- 10An object of mass $0.5\, {kg}$ is executing simple harmonic motion. Its amplitude is $5\, {cm}$ and time period (T) is $0.2\, {s} .$ What will be the potential energy of the object at an instant $t=\frac{T}{4}$ s starting from mean position. Assume that the initial phase of the oscillation is zero. (In ${J}$)View Solution