Oscillations & spring problem.

[teenholiday]

A massless sping of spring constant k=74 N/m is hanging from the ceiling. A 490g mass is hooked onto the unstretched spring and allowed to drop. Find the amplitude and the period of the resulting motion.

Attempt:
F= -kx

x= A cos (wt)
w = sqrt(k/m) t

I'm trying to solve for A, but how do I get rid of the t variable?


Thanks

 

[rock.freak667]

Find $\omega$ and you could use the fact that at max displacement from the equilibrium posistion, velocty=0.

 

[baba89]

for your question. In this problem, the t variable represents time, which is an important factor in determining the amplitude and period of the resulting motion. To solve for A, we can use the initial conditions of the problem.

At the beginning, the mass is at rest and the spring is unstretched. This means that the displacement (x) is equal to the amplitude (A).

Therefore, we can set x = A in the equation F = -kx and solve for A:

F = -kA
490g = -(74 N/m)A
A = (490g)/(-74 N/m) = -6.62 m

Note that the negative sign indicates that the displacement is in the opposite direction of the force.

To find the period, we can use the equation w = sqrt(k/m) and substitute the values for k and m:

w = sqrt(74 N/m / 0.490 kg) = 8.03 rad/s

The period (T) is defined as the time it takes for one complete oscillation, which can be calculated using the formula T = 2π/w:

T = 2π / (8.03 rad/s) = 0.785 s

Therefore, the amplitude of the resulting motion is -6.62 m and the period is 0.785 seconds.

I hope this helps! Let me know if you have any further questions.