(a) what is the length of a simple pendulum that oscillates with a period of 1.2 s on earth, where the acceleration due to gravity is 9.80 m/s2, and on mars, where the acceleration due to gravity is 3.70 m/s2?
le = m lm = m
(b) what mass would you need to suspend from a spring with a force constant of 20 n/m in order for the mass-spring system to oscillate with a period of 1.2 s on earth, where the acceleration due to gravity is 9.80 m/s2, and on mars, where the acceleration due to gravity is 3.70 m/s2?
me = kg mm = kg

a) Length of pendulum in Earth = 0.36 m      Length of pendulum in Mars = 0.13 mb) Mass in Earth = Mass in Mars = 0.73 kg

Explanation:

a) Period of simple pendulum

                 

   l₁ = length of pendulum in Earth = ?

   l₂ = length of pendulum in Mars = ?

   T = Period of pendulum = 1.2 s

    g₁ = Acceleration due to gravity in Earth = 9.80 m/s²

    g₂ = Acceleration due to gravity in Mars = 3.70 m/s²

For Earth :-

     

     Length of pendulum in Earth = 0.36 m      

For Mars :-

     

     Length of pendulum in Mars = 0.13 m

b) Period of spring

                 

 Here period is independent of acceleration due to gravity, so mass value is same in Earth and Mars.

                m = Mass = ?

                 T = Period = 1.2 s

                  k = Spring constant = 20 N/m

             

             Mass in Earth = Mass in Mars = 0.73 kg

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