00:01
This question, we're given that the mass is weighing four pounds, is attached to a spring, spring constant as 25 pounds per feet.
00:07
So we have to find the equation of the motion, given that g is 3 to feet per second square for the acceleration due to gravity, and t's to be measured in second, and then we have to find a period of the shm as well.
00:19
So if this is a simple harmonic motion, this means that the acceleration or the force, which is ma, is directly proportional to the displacement of the spring.
00:27
So that is equal to minus of kx because the force and mass force and the space are opposite to each other.
00:35
You know that acceleration is d square x over dt square.
00:38
So this is equal to minus kx.
00:40
Now the mass is nothing but weight is already given.
00:43
So mass is what? weight over gravity, which is 32 feet per second per second square.
00:49
So it's 4 over 32 times d square x over dt square and k is already given as 25...