a particle executing shm time period t from mean position the time to complete 5/8 oscillation
To find the time it takes for a particle executing Simple Harmonic Motion (SHM) to complete a certain fraction of an oscillation, we need to use the formula for the time period of SHM.
The time period (T) of SHM is the time it takes for one complete oscillation. It is given by the formula:
T = 2π√(m/k)
Where:
- T: Time period of SHM
- π: Pi (approximately 3.14159)
- m: Mass of the particle
- k: Spring constant
Since the given information does not provide the values of mass (m) and spring constant (k), we cannot directly calculate the time period. However, if we assume these values are constant, we can still find the time it takes to complete 5/8 of an oscillation.
Let's analyze the situation step by step:
1. Calculate the time period (T) using the given information, or assume a specific value for mass (m) and spring constant (k).
2. Divide the time period (T) by the number of oscillations completed in that time period. In this case, we want to find the time it takes to complete 5/8 of an oscillation. Therefore, we divide the time period (T) by 5/8.
3. Multiply the result by 5 to find the time it takes to complete 5/8 of an oscillation.
Keep in mind that this approach assumes the mass and spring constant are constant throughout the motion.
ok, assumeing harmonic motion along x axis, then x=sin(wt)
when x=-1/8, then
-.125=sin(wt)
wt=arcsin(-.125)=187 degrees
now, the time to do that depends on angular frequency w.