Advertisements
Advertisements
प्रश्न
A particle executes simple harmonic motion under the restoring force provided by a spring. The time period is T. If the spring is divided in two equal parts and one part is used to continue the simple harmonic motion, the time period will
विकल्प
remain T
become 2T
become T/2
become \[T/\sqrt{2}\]
Advertisements
उत्तर
become \[T/\sqrt{2}\]
Time period \[\left( T \right)\] is given by,
\[T = 2\pi\sqrt{\frac{m}{k}}\]
where m is the mass, and
k is spring constant.
When the spring is divided into two parts, the new spring constant k1 is given as,
k1 =\[2k\]
New time period T1 :
T1 = \[2\pi\sqrt{\frac{m}{2k}} = \frac{1}{\sqrt{2}}2\pi\sqrt{\frac{m}{k}} = \frac{1}{\sqrt{2}}T\]
APPEARS IN
संबंधित प्रश्न
A copper metal cube has each side of length 1 m. The bottom edge of the cube is fixed and tangential force 4.2x108 N is applied to a top surface. Calculate the lateral displacement of the top surface if modulus of rigidity of copper is 14x1010 N/m2.
Which of the following example represent periodic motion?
An arrow released from a bow.
Figure depicts four x-t plots for linear motion of a particle. Which of the plots represent periodic motion? What is the period of motion (in case of periodic motion)?
The length of the second’s pendulum in a clock is increased to 4 times its initial length. Calculate the number of oscillations completed by the new pendulum in one minute.
The total mechanical energy of a spring-mass system in simple harmonic motion is \[E = \frac{1}{2}m \omega^2 A^2 .\] Suppose the oscillating particle is replaced by another particle of double the mass while the amplitude A remains the same. The new mechanical energy will
A particle executes simple harmonic motion with a frequency v. The frequency with which the kinetic energy oscillates is
Two bodies A and B of equal mass are suspended from two separate massless springs of spring constant k1 and k2 respectively. If the bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitude of A to that of B is
A spring stores 5 J of energy when stretched by 25 cm. It is kept vertical with the lower end fixed. A block fastened to its other end is made to undergo small oscillations. If the block makes 5 oscillations each second what is the mass of the block?
A small block of mass m is kept on a bigger block of mass M which is attached to a vertical spring of spring constant k as shown in the figure. The system oscillates vertically. (a) Find the resultant force on the smaller block when it is displaced through a distance x above its equilibrium position. (b) Find the normal force on the smaller block at this position. When is this force smallest in magnitude? (c) What can be the maximum amplitude with which the two blocks may oscillate together?
A particle of mass m is attatched to three springs A, B and C of equal force constants kas shown in figure . If the particle is pushed slightly against the spring C and released, find the time period of oscillation.
The string the spring and the pulley shown in figure are light. Find the time period of the mass m.
The left block in figure moves at a speed v towards the right block placed in equilibrium. All collisions to take place are elastic and the surfaces are frictionless. Show that the motions of the two blocks are periodic. Find the time period of these periodic motions. Neglect the widths of the blocks.
A 20 cm wide thin circular disc of mass 200 g is suspended to rigid support from a thin metallic string. By holding the rim of the disc, the string is twisted through 60° and released. It now performs angular oscillations of period 1 second. Calculate the maximum restoring torque generated in the string under undamped conditions. (π3 ≈ 31)
Find the number of oscillations performed per minute by a magnet is vibrating in the plane of a uniform field of 1.6 × 10-5 Wb/m2. The magnet has a moment of inertia 3 × 10-6 kg/m2 and magnetic moment 3 A m2.
Which of the following example represent periodic motion?
A swimmer completing one (return) trip from one bank of a river to the other and back.
A simple pendulum of frequency n falls freely under gravity from a certain height from the ground level. Its frequency of oscillation.
Show that the motion of a particle represented by y = sin ωt – cos ωt is simple harmonic with a period of 2π/ω.
The time period of a simple pendulum is T inside a lift when the lift is stationary. If the lift moves upwards with an acceleration `g/2`, the time period of the pendulum will be ______.
A particle performs simple harmonic motion with a period of 2 seconds. The time taken by the particle to cover a displacement equal to half of its amplitude from the mean position is `1/a` s. The value of 'a' to the nearest integer is ______.
