1. Condition for losing contact

A washer resting on a vertically oscillating piston will lose contact when the normal reaction becomes zero.

While in contact, the washer has the same acceleration as the piston.

For vertical SHM, $a = -\omega^2 y$ The maximum downward acceleration occurs at the topmost position: $a_{\max} = \omega^2 A$

The washer just loses contact when this downward acceleration equals gravitational acceleration: $\omega^2 A = g$

2. Substitute the given amplitude

Amplitude: $A = 7\text{ cm} = 0.07\text{ m}$

So, $\omega = \sqrt{\frac{g}{A}} = \sqrt{\frac{9.8}{0.07}}$

$\omega = \sqrt{140} \approx 11.83\text{ rad/s}$

3. Convert angular frequency to frequency

Using $f = \frac{\omega}{2\pi}$

$f = \frac{11.83}{2\pi} \approx \frac{11.83}{6.283} \approx 1.88\text{ Hz}$

Thus the required frequency is close to $f \approx 1.9\text{ Hz}$

4. Check options

• A: $0.1\,$Hz ❌
• B: $1.2\,$Hz ❌
• C: $0.7\,$Hz ❌
• D: $1.9\,$Hz ✅

Therefore, the correct option is D.