In a simple harmonic motion

The force which tries to bring a body back to its mean position is called :

A particle executes $SHM$ with a time period of $16\ s$. At time $t=2\ s$, the particle crosses the mean position while at $t=4s$, its velocity is $4ms^{-1}$. The amplitude of motion in meter is:

The particle is executing S.H.M. on a line 4 cms long. If its velocity at its mean position is 12 cm/sec, its frequency in Hertz will be :

An object is attached to the bottom of a light vertical spring and set vibrating. The maximum speed of the object is 15 ${ cms }^{ -1 }$ and the period is 628 milli-seconds. The amplitude of the motion in centimeters is :

The different equation for linear SHM of a partial of mass $2g$ is $\dfrac {d^{2}x}{dt^{2}} + 16x = 0$. Find the force constant. $[K = mw^{2}]$.

If a body mass $36 gm$ moves with S,H,M of amplitude $A=13$ and period  $T=12 sec$. At a time $t=0$ the displacement is $x=+13 cm$. The shortest time of passage from $x=+6.5$ cm to $x=-6.5$ is

A function of time given by $\left(\sin{\omega t}-\cos{\omega t}\right)$ represents

A particle is subjected to two simple harmonic motions along $x$ and $y$ directions according to $x=3\sin\ 100\pi t$ $y=4\sin\ 100\pi t$

A ring whose diameter is 1 meter, oscillates simple harmonically in a vertical plane about a nail fixed at its circumference and perpendicular to plane of ring. The time period will be

The graph between restoring force and time in case of SHM is a

A person weighing $60\ kg$ stands on a platform which oscillates up and down at a frequency of $2\ Hz$ and amplitude $5\ cm$. The maximum and minimum apparent weights are nearly: ($g$ = 10$\ m/s^2$)

A body of mass $0.5$ kg is performing S.H.M. with a time period $\pi /2$ seconds. If its velocity at mean position is $1$ m/s, the restoring force acts on the body at a phase angle $60^o$ from extreme position is

Assertion : If a block is in SHM, and a new constant force acts in the direction of change, the mean position may change.
Reason :In SHM only variable forces should act on the body, for example spring force.

Sitar maestro Ravi Shankar is playing sitar on its strings, and you, as a physicist (unfortunately without musical ears!), observed the following oddities.
I. The greater the length of a vibrating string, the smaller its frequency.
II. The greater the tension in the string, the greater is the frequency.
III. The heavier the mass of the string, the smaller the frequency.
IV. The thinner the wire, the higher its frequency.
The maestro signalled the following combination as correct one.

Three similar oscillators, A, B, C have the same small damping constant $r$, but different natural frequencies $\omega _0 = (k/m)^{\frac{1}{2}} : 1200 Hz, 1800 Hz, 2400 Hz$. If all three are driven by the same source at $1800 Hz$, which statement is correct for the phases of the velocities of the three?

A stretched string of one meter length, fixed at both the ends having mass of $5 \times 10^{-4}$ kg is under tension of 20 N. It is plucked at a point situated 25 cm from one end. The stretched string would vibrate with the frequency of:

Speed v of a particle moving along a straight line, when it is at a distance x from a fixed point on the line is given by $V^2=108-9x^2$(all quantities in S. I. unit). Then

The equation of motion of a particle of mass $1$ g is $\frac{{{d^2}x}}{{d{t^2}}} + {\pi ^2}x = 0$ where $x$ is displacement (in m) from mean position. The frequency of oscillation is ( in Hz):

A planck with a body of mass m placed on to it starts moving straight up with the law $y=a(1-\cos{\omega t})$ where $\omega$ is displacement. Find the time dependent force:

The frequency of a seconds pendulum is equal to :

The time taken to complete $20$ oscillations by a seconds pendulum is: 

The length of a second's pendulum on the surface of the earth is equal to 99.49 cm. True or false.

If R is the radius of the earth and g the acceleration due to gravity on the earth's surface, the mean density of the earth is

Let the time period of a seconds pendulum is $2.5\ s.$ Tell by how much time will the clock behind in $10\ hrs.$

The mass of a bob, suspended in a simple pendulum, is halved from the initial mass, its time period will :

If the length of a seconds pendulum is increased by $2$% then what is loss and gain in a day?

If the length of second's pendulum is increased by $2\%$, how many second will it lose per day?

The different equation of simple harmonic motion for a seconds pendulum is:

A simple pendulum with a bob of mass m swings with an angular amplitude of ${ 60 }^{ 0 }$, when its angular displacement is ${ 30 }^{ 0 }$, the tension of string would be 

The simple pendulum acts as second's pendulum on earth. Its time on a planet, whose mass and diameter are twice that of earth is:

The length of a second's pendulum at a place where g = 9.8m/s $\displaystyle ^{2}$ is 90.2 cm. State whether true or false.

A second's pendulum can be used as a timing device

The length of a second pendulum at the surface of earth is $1\ m$. The length of second pendulum at the surface of moon, where $g$ is $\dfrac{1}{6} th$ that of earth's surface.

The length of the simple pendulum which ticks seconds is:

A second's pendulum is mounted in a rocket. Its period of oscillation will decrease when the rocket is:

When a rigid body is suspended vertically and it oscillates with a small amplitude under the action of the force of gravity, the body is known as

 The amplitude of a simple pendulum, oscillating in air with a small spherical bob, decreases from $10\ cm$ to $8\ cm$ In $40$ seconds. Assuming that Stokes law is valid, and ratio of the coefficient of viscosity of air to that of carbon dioxide is $1.3$, the time In which amplitude of this pendulum will reduce from $10\ cm$ to $5\ cm$ in carbondioxide will be close to (in $5=1.601, \ln { 2 }  2=0.693$)

The time taken for 20 complete oscillations by a seconds pendulum is :

A hollow pendulum bob filled with water has a small hole at the bottom through which water escapes at a constant rate. Which of the following statements describes the variation of the time period (T) of the pendulum as the water flows out?

The frequency of a second's pendulum is

The frequency of a second's pendulum is :

A simple pendulum with length $L$ and mass $m$ of the bob is oscillating with an amplitude $a$. 

There is a clock which gives correct time at $20^o$C is subjected to $40^o$C. The coefficient of linear expansion of the pendulum is $12\times 10^{-6}$ per $^oC$, how much is gain or loss in time?

Find the length of a simple pendulum such that its time period is $2\ s$.

A desktop toy pendulum swings back and forth once every $1.0 s$. How long is this pendulum?

You are designing a pendulum clock to have a period of $1.0\ s$. How long should the pendulum be ?

Two pendulums of lengths 121 cm and 100 cm start vibrating at the same instant. They are in the mean position and in the same phase. After how many vibrations of the shorter pendulum, the two will be in the same phase in the mean position? 

Assertion (A): A wooden cube of side a floats in a non viscous liquid of density r. When it is slightly pressed and released, then it executes SHM
Reason (R): The net force responsible for SHM is the resultant of buoyancy force and true weight of the body.

A body is broken into two parts of masses $m _1$ and $m _2$ These parts are then separated by a distance r ,What is the value of $m _1/m _2$ so that the gravitational force has maximum possible value?

A person normally weighing 60kg stands on a platform which oscillates up and down simple harmonically with a frequency $2Hz$ and an amplitude $5cm$.if a machine on the platform gives the person's weight,then consider the following statements :

If a tunnel is cut at any orientation through earth, then in what time will, a ball released from one end, reach the other end (neglect the rotation of the earth) ?

A ball is in simple harmonic motion in a tunnel through center of the earth. Magnitude of gravitational force acting on the ball of radius $ y _o $ ,when it is at a distance $x$ from mean position is :

A solid cube of side $a$ and density $\rho _{0}$ floats on the surface of a liquid of density $\rho $. If the cube is slightly pushed downward, then it oscillates simple harmonically with a period of:

A ball is in simple harmonic motion in a tunnel through center of the earth. Total force that acts on the ball when it is at a distance $x$ from mean position is :

Suppose a tunnel is dug along a diameter of the earth. A particle is dropped from a point, a distance $h$ directly above the tunnel, the motion of the particle is

A small ball of density $\rho _{0}$ is released from rest from the surface of a liquid whose density varies with depth $h$ as $\rho =\dfrac{\rho _{0}}{2}(a+\beta h)$Mass of the ball is $m$.Select the most appropriate option:

A cylindrical block of wood $(density=650 kg m^{-3})$, of base area $30 cm^2$ and height $54 cm$, floats in a liquid of density $900 kg$ $m^{-3}$. The block is depressed slightly and then released. The time period of the resulting oscillations of the block would be equal to that of a simple pendulum of length (nearly)