Calculate Max Acceleration Mass-Spring System: Vibration/SHM Help

[hshphyss]

Can anyone help me with this problem? Thank-you

1) A mass-spring system oscillates with an amplitude of 3.5 cm. The spring constant is 230 N/m and the mass is 0.50 kg. The
mechanical energy of the mass-spring system is 0.14 joules. Calculate the maximum acceleration of the mass-spring system.

I'm not sure what formula I would use... am I solving for g?

 

[Astronuc]

The problem is asking for the maximum acceleration of the mass-spring system, and acceleration, a, = dv/dt.

One is given the spring constant, k, and mass, m, from which one may obtain the angular frequency,$\omega$, of the system.

One is also given the maximum amplitude.

Taking x(t) of the spring, which is the position of the mass from equilibrium, one can fine dx/dt, and d²x/dt².

 

[quicknote]

I would be happy to help you with this problem. To calculate the maximum acceleration of a mass-spring system, we can use the formula a = -ω^2x, where a is the acceleration, ω is the angular frequency, and x is the displacement from equilibrium. In this case, we can calculate the angular frequency using the formula ω = √(k/m), where k is the spring constant and m is the mass. Plugging in the given values, we get ω = √(230 N/m / 0.50 kg) = 10.77 rad/s.

Next, we can use the given amplitude to find the displacement from equilibrium, which is half of the amplitude. So x = 3.5 cm / 2 = 1.75 cm = 0.0175 m.

Finally, we can plug in these values into the formula for acceleration to get a = -(10.77 rad/s)^2 * 0.0175 m = -1.86 m/s^2.

Therefore, the maximum acceleration of the mass-spring system is 1.86 m/s^2.

I hope this helps! It is always important to carefully read the problem and identify which formulas and values are needed to solve it.