. Which of the following combinations of variables results in the greatest perio

Question

. Which of the following combinations of variables results in the greatest period for a pendulum? length = L, mass = M, and maximum angular displacement = 3 degrees Length 2L, mass = M/2, and maximum angular displacement = 1 degree length = 1 .5L, mass = 2M, and maximum angular displacement = 2 degrees length root 2 L, mass = root 2 M and maximum angular displacement = root 2 degrees length = root 3 L, mass = 4M, and maximum angular displacement = 4 degrees 3. To double the total energy of a mass oscillating at the end of a spring with amplitude A, we need to increase the angular frequency by root 2. increase the amplitude by root 2 increase the amplitude by 2. increase the angular frequency by 2. increase the amplitude by 4 and decrease the angular frequency by 1/ root 2

Explanation / Answer

2)

time period of a pendulum=2*pi(L/g)1/2

since time period only depends on L

so it will be maximum for largest length

so option 2) with 2L is correct

3)

total energy=kA2/2

if we increase amplitude to 21/2A

total energy will become double

so option 2) is correct

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