A struck bell is an underdamped oscillator: displace it and it rings, the amplitude fading as friction bleeds the energy away.
A hammer blow is idealised as a Dirac delta — an infinitely brief force that leaves the position unchanged but jumps the velocity. The bell's answer to one unit kick is its impulse response: a single damped sinusoid.
Because the equation is linear, many blows just add their shifted impulse responses (Duhamel's principle). Land them one period apart and they reinforce — resonance by percussion.
Strike once, dead against the swing, with a blow that exactly matches the current velocity, and the sum collapses to zero: position zero, velocity zero, silence. One delta erases the ring.