Two different simple harmonic oscillators havethe same natural frequency (f=3.00

Question

Two different simple harmonic oscillators havethe same natural frequency (f=3.00 Hz) when they are on the surfaceof the Earth. The first oscillator is a pendulum, the second is avertical spring and mass. If both systems are moved to the surfaceof the moon (g=1.67 m/s2), what is the new frequency ofthe vertical spring and mass? Calculate the new frequency of thependulum. Two different simple harmonic oscillators havethe same natural frequency (f=3.00 Hz) when they are on the surfaceof the Earth. The first oscillator is a pendulum, the second is avertical spring and mass. If both systems are moved to the surfaceof the moon (g=1.67 m/s2), what is the new frequency ofthe vertical spring and mass? Calculate the new frequency of thependulum.

Explanation / Answer

   Frequency of spring masssystem      fs-m   =   (1/2)* (k/m)    Frequency of simplependulum         fp   =   (1/2)* (l/g)    a.   Since neither springconstant (k) nor mass suspended (m) depends upon the accelerationdue to gravity, the frequency of spring mass oscillator will remainthe same on the Moon.    fs-m'   =   3.00   Hz    b.   on the surface ofearth      fp   =   (1/2)* (l/9.8)          on thesurface ofMoon   fp'   =   (1/2)* (l/1.67)          dividing      fp'/ fp   =   (1.67 /9.8)          frequency ofsimple pendulum on Moonsurface      fp'   =   3.00* (1.67 / 9.8)                                                                                                          =   1.24   Hz                                                                             

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