A particle vibrates in Simple Harmonic Motion with amplitude. What will be its displacement in one time-period
if you attach a mass to the spring from its initial equilibrium position, it vibrates forever in simple harmonic motion. Why doesn't it come to rest after stretching by a distance 'd'; proportional to the weight of the mass, when the spring's restoring force cancels out the weight of the mass? How will you measure the equilibrium position? How can you attach the mass to the spring so that it doesn't oscillate when you let go?
dislacement? zero, it ends where it started.
The second paragraph requires some thinking. I will be happy to critique your thinking, but won't do it for you.
k but i really don't understand this topic at all...
To find the displacement of the particle in one time-period of Simple Harmonic Motion (SHM) with a given amplitude, you can use the relationship between amplitude and displacement. The displacement of a particle in SHM is given by the equation:
x = A * cos(ωt)
Where:
- x is the displacement of the particle at time t,
- A is the amplitude of the SHM, and
- ω is the angular frequency of the SHM, given by ω = 2π/T, where T is the time-period.
Since the function is periodic with a time-period, T, the displacement of the particle at time T will be the same as its initial displacement, given by x = A * cos(0) = A.
Therefore, the displacement of the particle in one time-period of SHM with a given amplitude is equal to the amplitude itself.
Now, let's address the second question about why a mass attached to a spring in SHM does not come to rest when the spring's restoring force cancels out the weight of the mass. In SHM, the restoring force of the spring only cancels out the weight of the mass at the equilibrium position. However, the mass will still possess kinetic energy due to its inertia, causing it to continue oscillating back and forth around the equilibrium position. Therefore, even though the net force on the mass is zero at the equilibrium point due to the balance between the weight and the restoring force of the spring, the mass will not come to rest.
To measure the equilibrium position, one way is to note the position where the mass attached to the spring comes to a stable, stationary position. This is the point where the restoring force of the spring accurately opposes the weight of the mass, resulting in a net force of zero.
To attach the mass to the spring in a way that it doesn't oscillate when you let go, you need to carefully position the mass at the equilibrium position and secure it to the spring without imparting any additional energy or motion. This can be achieved by fixing the mass securely to the spring without causing any sideways or downward displacements.