Advertisements
Advertisements
Question
Which of the following quantities are always negative in a simple harmonic motion?
(a) \[\vec{F} . \vec{a} .\]
(b) \[\vec{v} . \vec{r} .\]
(c) \[\vec{a} . \vec{r} .\]
(d)\[\vec{F} . \vec{r} .\]
Advertisements
Solution
(c) \[\vec{a} . \vec{r} .\]
(d)\[\vec{F} . \vec{r} .\]
In S.H.M.,
F = -kx
Therefore,
\[\vec{F} . \vec{r} .\] will always be negative. As acceleration has the same direction as the force,
\[\vec{a} . \vec{r} \] Will also be negative , always .
APPEARS IN
RELATED QUESTIONS
A particle executes S.H.M. with a period of 10 seconds. Find the time in which its potential energy will be half of its total energy.
State the differential equation of linear simple harmonic motion.
A small creature moves with constant speed in a vertical circle on a bright day. Does its shadow formed by the sun on a horizontal plane move in a sample harmonic motion?
The time period of a particle in simple harmonic motion is equal to the time between consecutive appearances of the particle at a particular point in its motion. This point is
The displacement of a particle in simple harmonic motion in one time period is
The distance moved by a particle in simple harmonic motion in one time period is
The displacement of a particle is given by \[\overrightarrow{r} = A\left( \overrightarrow{i} \cos\omega t + \overrightarrow{j} \sin\omega t \right) .\] The motion of the particle is
Figure represents two simple harmonic motions.
The parameter which has different values in the two motions is
A pendulum clock keeping correct time is taken to high altitudes,
A particle moves in a circular path with a continuously increasing speed. Its motion is
A particle moves on the X-axis according to the equation x = x0 sin2 ωt. The motion is simple harmonic
Which of the following will change the time period as they are taken to moon?
(a) A simple pendulum
(b) A physical pendulum
(c) A torsional pendulum
(d) A spring-mass system
Assume that a tunnel is dug along a chord of the earth, at a perpendicular distance R/2 from the earth's centre where R is the radius of the earth. The wall of the tunnel is frictionless. (a) Find the gravitational force exerted by the earth on a particle of mass mplaced in the tunnel at a distance x from the centre of the tunnel. (b) Find the component of this force along the tunnel and perpendicular to the tunnel. (c) Find the normal force exerted by the wall on the particle. (d) Find the resultant force on the particle. (e) Show that the motion of the particle in the tunnel is simple harmonic and find the time period.
A simple pendulum of length l is suspended through the ceiling of an elevator. Find the time period of small oscillations if the elevator (a) is going up with and acceleration a0(b) is going down with an acceleration a0 and (c) is moving with a uniform velocity.
A simple pendulum of length 1 feet suspended from the ceiling of an elevator takes π/3 seconds to complete one oscillation. Find the acceleration of the elevator.
A simple pendulum fixed in a car has a time period of 4 seconds when the car is moving uniformly on a horizontal road. When the accelerator is pressed, the time period changes to 3.99 seconds. Making an approximate analysis, find the acceleration of the car.
Three simple harmonic motions of equal amplitude A and equal time periods in the same direction combine. The phase of the second motion is 60° ahead of the first and the phase of the third motion is 60° ahead of the second. Find the amplitude of the resultant motion.
Write short notes on two springs connected in series.
Consider a simple pendulum of length l = 0.9 m which is properly placed on a trolley rolling down on a inclined plane which is at θ = 45° with the horizontal. Assuming that the inclined plane is frictionless, calculate the time period of oscillation of the simple pendulum.
A body having specific charge 8 µC/g is resting on a frictionless plane at a distance 10 cm from the wall (as shown in the figure). It starts moving towards the wall when a uniform electric field of 100 V/m is applied horizontally toward the wall. If the collision of the body with the wall is perfectly elastic, then the time period of the motion will be ______ s.
