Question 1 Asimpie pendulums time period of free undamped vi

Question 1 Asimpie pendulum\'s time period of free undamped vibrations is determined to be 0.63 seconds.if the gravitational acceleration is 9.8 m/sec2 what is the length of the pendulum in meters? Moving to another question will save this response. Question 2 acement of tom has a natural frequency of 3 radisec What will be its natural frequency if t is given an initial displacement of o a o rad/sec O c 3 rad/sec d. 1.5 rad/sec Moving to another ouestion will save this response Moving to another question will save this response, Question 3 in a mass soring ystem, ifthe massis decreased what happens to the time peried of free uncamped vibratons? o a Time period remains the same b. Time period increases g G Time period bécomes zero e d. Time period decreases

Solution

Ans- a) Given- T= 0.63 sec, g= 9.8 m/s^2

We know Time period of a simple pendulum is given by- T= 2*pi*(L/g)^(1/2)

0.63 = 2*pi*(L/9.8)^(1/2)

L = (0.63/2*pi)^2 * 9.8

L = .0985 m.

b) The natural frequency is independent of the initial displacement. Thus It will be 3 rad/sec for the second case also.

c) The formula for the time period is T= 2*pi*(m/k)^1/2. Thus if the mass is decreased time period will also decrease as it is proportional to m^(1/2).