###### Advertisements

###### Advertisements

The period of oscillation of a body of mass m_{1} suspended from a light spring is T. When a body of mass m_{2} is tied to the first body and the system is made to oscillate, the period is 2T. Compare the masses m_{1} and m_{2}

###### Advertisements

#### Solution

T = `2πsqrt("m"/"k")`

∴ `(2"T")/"T"` = 2 = `sqrt(("m"_1+"m"_2)/"m"_1)`

∴ `("m"_1+"m"_2)/"m"_1` = 4

∴ `"m"_2/"m"_1=3/1`

∴ `"m"_1/"m"_2=1/3`

This gives the required ratio of the masses.

#### APPEARS IN

#### RELATED QUESTIONS

A seconds pendulum is suspended in an elevator moving with constant speed in downward direction. The periodic time (T) of that pendulum is _______.

The periodic time of a linear harmonic oscillator is 2π second, with maximum displacement of 1 cm. If the particle starts from extreme position, find the displacement of the particle after π/3 seconds.

A copper metal cube has each side of length 1 m. The bottom edge of the cube is fixed and tangential force 4.2x10^{8} N is applied to a top surface. Calculate the lateral displacement of the top surface if modulus of rigidity of copper is 14x10^{10} N/m^{2}.

**Answer in brief:**

Derive an expression for the period of motion of a simple pendulum. On which factors does it depend?

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.

A person goes to bed at sharp 10.00 pm every day. Is it an example of periodic motion? If yes, what is the time period? If no, why?

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 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

Two bodies *A* and *B* of equal mass are suspended from two separate massless springs of spring constant *k*_{1} and *k*_{2} 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 particle is fastened at the end of a string and is whirled in a vertical circle with the other end of the string being fixed. The motion of the particle is

The position, velocity and acceleration of a particle executing simple harmonic motion are found to have magnitude 2 cm, 1 m s^{−1} and 10 m s^{−2} at a certain instant. Find the amplitude and the time period of the motion.

Consider a simple harmonic motion of time period T. Calculate the time taken for the displacement to change value from half the amplitude to the amplitude.

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?

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.

Find the time period of the motion of the particle shown in figure . Neglect the small effect of the bend near the bottom.

A uniform disc of radius *r* is to be suspended through a small hole made in the disc. Find the minimum possible time period of the disc for small oscillations. What should be the distance of the hole from the centre for it to have minimum time period?

A body of mass 1 kg is mafe to oscillate on a spring of force constant 16 N/m. Calculate (a) Angular frequency, (b) Frequency of vibrations.

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. (π^{3} ≈ 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/m^{2}. The magnet has a moment of inertia 3 × 10^{-6} kg/m^{2} and magnetic moment 3 A m^{2}.

The maximum speed of a particle executing S.H.M. is 10 m/s and maximum acceleration is 31.4 m/s^{2}. Its periodic time is ______

A simple pendulum is inside a spacecraft. What will be its periodic time?

**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.

**Which of the following example represent periodic motion?**

A hydrogen molecule rotating about its center of mass.

**Which of the following example represent (nearly) simple harmonic motion and which represent periodic but not simple harmonic motion?**

A motion of an oscillating mercury column in a U-tube.

When two displacements represented by y_{1} = a sin(ωt) and y_{2 }= b cos(ωt) are superimposed the motion is ______.

A simple pendulum of frequency n falls freely under gravity from a certain height from the ground level. Its frequency of oscillation.

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 ______.

When a particle executes Simple Harmonic Motion, the nature of the graph of velocity as a function of displacement 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 ______.