Q.1.A spring of force constant'k'is cut into two parts whoose lengths are in the ratio 1:2.The parts are now connected in paralle and a block of mass'm'is suspended at the end of the combined spring.Find the period of oscillation performed by the block.
Q.2.The angle (in radians) made by the string of simple pendulum with the vertical depends on time as TEETHA = (pi/90)sin[(pi/sec)t].Find the length of the pendulum if g = (pi.pi) i.e. pi sqare meter per second sqare.
Q1. A numerical value for the peiod cannot be provided without numerical values for the mass m and original spring constant, k. Before cutting aqnd rearranging, the period was
P1 = 2 pi sqrt (m/k)
After cutting, the two springs have sping constants 3k (short spring) and (3k/2) (long spring). When arranged in parallel, the spring constants add to give an effective spring constant of 9k/2. The new period is
P2 = 2 pi sqrt[(2/9)(m/k)]
= (sqrt2)/3 * P1
Q2. I don't understand the meaning of (pi/sec)t as the argument of the sin function.
If the angle argument is pi*t, with t in seconds, then sqrt(g/L) = w = pi (sec^-1)
where w is the angular frequency, which equals sqrt (g/L)
If g = pi^2 (m/s^2), then
g/L = pi^2 = pi^2/L
so L = 1 m