Spring oscillations, restoring force, force constant
- In an oscillating spring mass system, a spring is connected to a box filled with sand. As the box oscillates, sand leaks slowly out of the box vertically so that the average frequency ω(t) and average amplitude A(t) of the system change with time t.… Answer: 2. Graph pair: ω(t) rises and saturates; A(t) decays Key idea: the frequency of a spring-mass system is ω=√(k/m) , and sand leaking... 1
- A spring is stretched by 5 cm by a force 10 N. The time period of the oscillations when a mass of 2 kg is suspended by it is : Answer: 4. 0.628 s Key idea: find k from the stretch, then use T=2π√(m/k) . k=F/x=10/0.05=200\ N/m T=2π√(2/200)=2π×0.1=0.628\ mathrm s . Opt... 1
- A spring of force constant k is cut into lengths of ratio 1 : 2 : 3. They are connected in series and the new force constant is k'. Then they are connected in parallel and force constant is k''. Then k' : k'' is : Answer: 2. 1 : 11 Key idea: spring constant is inversely proportional to length. Pieces have lengths L/6,L/3,L/2 , so constants 6k,3k,2k . S... 1
- A body of mass m is attached to the lower end of a spring whose upper end is fixed. The spring has negligible mass. When the mass m is slightly pulled down and released, it oscillates with a time period of 3 s. When the mass m is increased by 1 kg, t… Answer: 3. 9/16 Time period of a spring-mass system is T=2π√(m/k) , so T²∝ m . T₁²/T₂²=m/m+1⇒9/25=m/m+1 9m+9=25m , so 16m=9 and m=9/16 kg. O... 1