A vertical elastic suspension tether has a stiffness constant k=1.20 N cm−1k = 1.20\text{ N cm}^{-1}k=1.20 N cm−1.
A research probe of mass 0.60 kg0.60\text{ kg}0.60 kg is attached to the bottom end of the tether, with the top end fixed to a rigid mounting plate.
In position A, the probe rests in equilibrium, and the extension of the tether is 5.0 cm5.0\text{ cm}5.0 cm.
In position B, an external downward force FFF is applied to the probe so that it rests at a distance ddd below its equilibrium position. The extension of the tether in this position is 13.5 cm13.5\text{ cm}13.5 cm.
The force FFF is suddenly released.
Calculate the magnitude of the probe's initial acceleration at the instant the force FFF is removed. Assume the tether does not exceed its limit of proportionality.
The probe subsequently undergoes simple harmonic motion. Calculate the frequency of this oscillation.
The probe is now replaced by a steel test cylinder of mass 0.45 kg0.45\text{ kg}0.45 kg, which is positioned inside an electromagnetic driver. The driver is connected to a variable frequency signal generator that can excite the system at frequencies between 0.4 Hz0.4\text{ Hz}0.4 Hz and 4.0 Hz4.0\text{ Hz}4.0 Hz.
Calculate the natural frequency of this new arrangement.
Describe how the amplitude of the cylinder's oscillations changes as the driving frequency of the generator is varied from 0.4 Hz0.4\text{ Hz}0.4 Hz to 4.0 Hz4.0\text{ Hz}4.0 Hz.
