a body of mass m hung in a particular spring execute shm if period 1seconds What period would be obtained?
a,using a body of mass 4m?
v=e/t
v=4m/1sec
v=4m/s
frequency = constant * sqrt (k/m)
4 times m is 1/2 frequency or TWICE the period
F = m a
F = -k x
m a = - k x
if simple harmonic motion
x = A sin (2 pi t/T)
v = A (2 pi/T) cos (2 pi t/T)
a = -A(2 pi/T)^2 sin (2 pi t/T)
= -(2 pi/T)^2 x
so
m (-2pi/T)^2 x= -k x
(T/2 pi)^2 = m/k
T = 2 pi sqrt(m/k)
To find the period of a simple harmonic motion (SHM) for a spring-mass system, we can use the equation:
T = 2π√(m/k),
where T is the period, m is the mass of the body, and k is the spring constant.
In this case, the given period is 1 second. Using this information, we can rearrange the equation to solve for the spring constant:
k = 4π²m/T².
Now we can calculate the new period when the mass is increased to 4m. Let's substitute the new mass value into the equation:
T' = 2π√(4m/k).
To find the new period, we need to determine the new spring constant, which is denoted as k'. We can rearrange the equation for k to solve for k':
k' = 4π²(4m)/T'².
By substituting the equation for T' into the equation for k', we can calculate the new spring constant. Then, we can substitute this value into the equation for the new period:
T' = 2π√(4m/k').
Now we can break down the steps to calculate the new period:
1. Calculate the spring constant, k:
k = 4π²m/T².
2. Calculate the new spring constant, k':
k' = 4π²(4m)/T'².
3. Calculate the new period, T':
T' = 2π√(4m/k').
By following these steps, we can find the period when using a body of mass 4m in the same spring-mass system.