00:01
Hello students in this question for the part a we have to set up the differential equation for the motion of free oscillation and calculate the period of such oscillation.
00:14
Okay, so the differential equation for the free oscillation is x double dot plus gamma x dot plus omega not square x this is equals to zero.
00:27
Okay, so this is the differential equation which is taken now the period of oscillation first of all, calculating the time period to calculate time period.
00:37
First of all, we have to calculate the omega.
00:40
So this omega, this is equal to omega not square, which is natural frequency minus gamma to square divided by four.
00:48
Okay.
00:49
And gamma, which is equal to b by m.
00:53
So can be written as omega not, which is equal to under root of k by m and gamma, which is equals to b by m so we can substitute these values here so omega this is equals to k by m minus b squared divided by 4 m square and this under root so substituting the values so k which is spring constant 80 newton per meter mass is 0 .2 kg minus b which is 4 newton meter inverse second and this whole square divided 4 m which is 0 .2 and this whole square and this whole under root.
01:31
So from here we get omega this is equals to 10 under root 3 radian per second...