Resonance in Simple Harmonic Motion:
Resonance occurs in a system undergoing simple harmonic motion when the frequency of an external force matches the natural frequency of the system. At resonance, the amplitude of the oscillation reaches its maximum value.

Explanation:
When a system is subjected to simple harmonic motion, it has a natural frequency at which it oscillates most efficiently. This natural frequency is determined by the mass and stiffness of the system.

At resonance, the frequency of the external force driving the system matches the natural frequency of the system. This causes the amplitude of the oscillation to increase significantly.

Zero Damping:
Damping refers to the dissipation of energy in a system, which can cause the amplitude of the oscillation to decrease over time. In the case of zero damping, there is no energy loss, and the system can oscillate indefinitely.

Amplitude at Resonance:
When a system with zero damping is driven at its natural frequency, the amplitude of the oscillation increases without bound. This means that the amplitude becomes infinite at resonance.

Explanation:
- At resonance, the driving frequency matches the natural frequency of the system.
- Since there is no damping, there is no energy loss in the system.
- As a result, the system can continue to absorb energy from the driving force and the amplitude of the oscillation increases.
- The system keeps gaining energy and the amplitude grows without any limit.
- Therefore, the amplitude of simple harmonic motion at resonance is infinite.

Conclusion:
In the ideal case of zero damping, the amplitude of simple harmonic motion at resonance is infinite. This is because the system can continuously absorb energy from the driving force without any energy loss.