Advertisements
Advertisements
प्रश्न
A particle moves in the X-Y plane according to the equation \[\overrightarrow{r} = \left( \overrightarrow{i} + 2 \overrightarrow{j} \right)A\cos\omega t .\]
The motion of the particle is
(a) on a straight line
(b) on an ellipse
(c) periodic
(d) simple harmonic
Advertisements
उत्तर
(a) on a straight line
(c) periodic
(d) simple harmonic
The given equation is a solution to the equation of simple harmonic motion. The amplitude is \[( \overrightarrow i + 2 \overrightarrow j)A\] , following equation of straight line y = mx + c. Also, a simple harmonic motion is periodic.
APPEARS IN
संबंधित प्रश्न
A particle in S.H.M. has a period of 2 seconds and amplitude of 10 cm. Calculate the acceleration when it is at 4 cm from its positive extreme position.
Which of the following relationships between the acceleration a and the displacement x of a particle involve simple harmonic motion?
(a) a = 0.7x
(b) a = –200x2
(c) a = –10x
(d) a = 100x3
A body of mass 1 kg is made to oscillate on a spring of force constant 16 N/m. Calculate:
a) Angular frequency
b) frequency of vibration.
A hollow sphere filled with water is used as the bob of a pendulum. Assume that the equation for simple pendulum is valid with the distance between the point of suspension and centre of mass of the bob acting as the effective length of the pendulum. If water slowly leaks out of the bob, how will the time period vary?
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
A particle moves on the X-axis according to the equation x = A + B sin ωt. The motion is simple harmonic with amplitude
Figure represents two simple harmonic motions.
The parameter which has different values in the two motions is
A particle moves in a circular path with a continuously increasing speed. Its motion is
All the surfaces shown in figure are frictionless. The mass of the care is M, that of the block is m and the spring has spring constant k. Initially the car and the block are at rest and the spring is stretched through a length x0 when the system is released. (a) Find the amplitudes of the simple harmonic motion of the block and of the care as seen from the road. (b) Find the time period(s) of the two simple harmonic motions.
The angle made by the string of a simple pendulum with the vertical depends on time as \[\theta = \frac{\pi}{90} \sin \left[ \left( \pi s^{- 1} \right)t \right]\] .Find the length of the pendulum if g = π2 m2.
A small block oscillates back and forth on a smooth concave surface of radius R in Figure. Find the time period of small oscillation.
A spherical ball of mass m and radius r rolls without slipping on a rough concave surface of large radius R. It makes small oscillations about the lowest point. Find the time period.
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.
A simple pendulum has a time period T1. When its point of suspension is moved vertically upwards according to as y = kt2, where y is the vertical distance covered and k = 1 ms−2, its time period becomes T2. Then, T `"T"_1^2/"T"_2^2` is (g = 10 ms−2)
Consider the Earth as a homogeneous sphere of radius R and a straight hole is bored in it through its centre. Show that a particle dropped into the hole will execute a simple harmonic motion such that its time period is
T = `2π sqrt("R"/"g")`
A simple harmonic motion is given by, x = 2.4 sin ( 4πt). If distances are expressed in cm and time in seconds, the amplitude and frequency of S.H.M. are respectively,
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.
The velocities of a particle in SHM at positions x1 and x2 are v1 and v2 respectively, its time period will be ______.
A weightless rigid rod with a small iron bob at the end is hinged at point A to the wall so that it can rotate in all directions. The rod is kept in the horizontal position by a vertical inextensible string of length 20 cm, fixed at its midpoint. The bob is displaced slightly, perpendicular to the plane of the rod and string. The period of small oscillations of the system in the form `(pix)/10` is ______ sec. and the value of x is ______.
(g = 10 m/s2)
