Contact, Friction, Detachment, and Sudden Changes
Across an ideal instantaneous event, position is continuous; momentum is conserved only for an isolated collision, while the post-event amplitude follows from the new equilibrium, frequency, position, and velocity.
Why this shows up in the exam
Mass added or removed during SHM · Blocks oscillating together without slipping · Washer detachment and maximum rise · Velocity kicks and oscillator-wall collisions
Learn the idea
During abrupt mass, speed, or contact changes, conserve only the quantities justified over the short event. An oscillator can change amplitude or equilibrium instantly after a collision, detachment, or mass change, but its position remains continuous and other quantities need separate conservation tests.
🧠 Memory hook: At the instant: keep position, then recheck momentum, equilibrium, and omega.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- A_new² = x_new² + (v_new/omega_new)² — post-event amplitude about the new equilibrium
- N = m(g + a_support) — normal force for vertical contact with a moving support
- |f_required| <= mu_s N — no-slip condition for stacked oscillating bodies
- Delta p_system = impulse_external — momentum test during a short interaction
How to approach it
- 1Split the motion into before, event, and after
- 2Apply only valid impulse or contact conditions
- 3Rebuild the post-event oscillator around its new equilibrium
Common slip-ups that cost marks
- •Conserving mechanical energy in a sticking collision
- •Keeping the old equilibrium after mass removal
- •Setting detachment at zero velocity instead of zero normal force
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A mass of 1 kg is attached to a spring of force constant 100 N/m. Find the angular frequency of small oscillations.
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