Home
Class 12
PHYSICS
If a simple harmonic motion is erpresent...

If a simple harmonic motion is erpresented by `(d^(2)x)/(dt^(2))+ax=0`,
its time period is.

A

`(2pi)/(alpha)`

B

`(2pi)/(sqrt(alpha))`

C

`2pialpha`

D

`2pisqrt(alpha)`

Text Solution

Verified by Experts

The correct Answer is:
B
`(d^(2)x)/(dt^(2)) + alphax = 0`
On comparing the above equation with the equation of SHM
`(d^(2)x)/(dt^(2)) + omega^(2)x = 0 rArr omega^(2) = a rArr omega =sqrt(alpha) rArr T = (2pi)/(sqrt(alpha))`
Promotional Banner

Topper's Solved these Questions

  • SIMPLE HARMONIC MOTION

    ALLEN|Exercise Exercise-05 [B]|12 Videos

  • SIMPLE HARMONIC MOTION

    ALLEN|Exercise MCQ s one or more than one correct answers|5 Videos

  • SIMPLE HARMONIC MOTION

    ALLEN|Exercise Exercise-04 [A]|20 Videos

  • RACE

    ALLEN|Exercise Basic Maths (Wave Motion & Dopplers Effect) (Stationary waves & doppler effect, beats)|25 Videos

  • TEST PAPER

    ALLEN|Exercise PHYSICS|4 Videos

Similar Questions

Explore conceptually related problems

If a simple harmonic motion is represented by (d^(2)x)/(dt^(2)) + alphax = 0 , its time period is :

If a simple harmonic motion is represented by (d^(2)x)/(dt^(2)) + alphax = 0 , its time period is :

A particle executes simple harmonic motion according to equation 4(d^(2)x)/(dt^(2))+320x=0 . Its time period of oscillation is :-

A sinple harmonic motion is represented by (d^2x)/(dt^2)+kx=0 , where k is a constant of the motion. Find its time period.

The equation of a simple harmonic motion of a particle is (d^(2)x)/(dt^(2)) + 0.2 (dx)/(dt) + 36x = 0 . Its time period is approximately

For a particle performing SHM , equation of motion is given as (d^(2))/(dt^(2)) + 4x = 0 . Find the time period

A particle is executing a linear S.H.M. and its differential equation is (d^(2)x)/(dt^(2))+ alpha x=0 . Its time period of motion is

Displacement 'x' of a simple harmonic oscillator varies with time, according to the differential equation (d^(2)x//dt^(2))+4x=0 . Then its time period is

The equation of a damped simple harmonic motion is 2m(d^(2)x)/(dt^(2))+2a_(0)(dx)/(dt)+kx=0 . Then the angualr frequency of oscillation is

A simple harmonic motion is represented by x=10sin(20t+0.5). Write down its amplitude, angular frequency, frequency, time period and initial phase if displacement is measured in metres and time seconds.

ALLEN-SIMPLE HARMONIC MOTION-Exercise-05 [A]
  1. The function sin^(2) (omegat) represents.

    Text Solution

    |

  2. Two simple harmonic are represented by the equation y(1)=0.1 sin (100p...

    Text Solution

    |

  3. If a simple harmonic motion is erpresented by (d^(2)x)/(dt^(2))+ax=0, ...

    Text Solution

    |

  4. The bob of a simple pendulum is a spherical hollow ball filled with wa...

    Text Solution

    |

  5. The maximum velocity a particle, executing simple harmonic motion with...

    Text Solution

    |

  6. Starting from the origin a body osillates simple harmonicall with a pe...

    Text Solution

    |

  7. The displacement of an obuect attached to a spring and executing simpl...

    Text Solution

    |

  8. A point mass oscillates along the x-axis according to the law x=x(0) c...

    Text Solution

    |

  9. If a simple pendulum has significant amplitude (up to a factor of (1)/...

    Text Solution

    |

  10. An ideal gas enclosed in a cylindrical container supports a freely mov...

    Text Solution

    |

  11. A particle moves with simple harmonic motion in a straight line. In fi...

    Text Solution

    |

  12. A pendulumd made of a uniform wire of cross sectional area (A) has tim...

    Text Solution

    |

  13. For a simple pendulum, a graph is plotted between itskinetic energy (K...

    Text Solution

    |

  14. A simple harmonic oscillator of angular frequency 2 "rad" s^(-1) is ac...

    Text Solution

    |

  15. A cylindrical of wood (density = 600 kg m^(-3)) of base area 30 cm^(2)...

    Text Solution

    |

  16. A pendulum with time period of 1s is losing energy due to damping. At ...

    Text Solution

    |

  17. A particle performs simple harmonic mition with amplitude A. Its speed...

    Text Solution

    |

  18. Two particles are in SHM in a straight line about same equilibrium pos...

    Text Solution

    |

  19. In an engine the piston undergoes vertical simple motion with amplitud...

    Text Solution

    |

  20. The bob of a simple pendulum executm simple harmonic motion in water w...

    Text Solution

    |