Standard +0.3 This is a straightforward SHM problem requiring standard formulas (ω = 2π/T, amplitude = 0.3m, F_max = mω²a) with direct substitution. While it's Further Maths content, it involves only routine application of well-known SHM relationships with no conceptual challenges or multi-step reasoning, making it slightly easier than average overall.
A particle \(P\), of mass \(0.2\) kg, moves in simple harmonic motion along a straight line under the action of a resultant force of magnitude \(F\) N. The distance between the end-points of the motion is \(0.6\) m, and the period of the motion is \(0.5\) s. Find the greatest value of \(F\) during the motion. [5]
Find ω or ω2 from 2π/T: ω = 2π / 0⋅5 [= 4π = 12⋅57] B1
Relate F to acceleration: F = 0⋅2 d 2 x/dt 2 M1
Relate acceleration to ω and x: d 2 x/dt 2 = [–]ω 2 x M1
State or use value of x giving max of F [or d 2 x/dt 2 ]: Maximum when x = [±] 0⋅3 M1
Evaluate maximum F of F: 0⋅2 (4π) 2 0⋅3 = 0⋅96π2 or 9⋅47 A1
Answer
Marks
Guidance
max
5
[5]
Question 1:
1 | Find ω or ω2 from 2π/T: ω = 2π / 0⋅5 [= 4π = 12⋅57] B1
Relate F to acceleration: F = 0⋅2 d 2 x/dt 2 M1
Relate acceleration to ω and x: d 2 x/dt 2 = [–]ω 2 x M1
State or use value of x giving max of F [or d 2 x/dt 2 ]: Maximum when x = [±] 0⋅3 M1
Evaluate maximum F of F: 0⋅2 (4π) 2 0⋅3 = 0⋅96π2 or 9⋅47 A1
max | 5 | [5]
A particle $P$, of mass $0.2$ kg, moves in simple harmonic motion along a straight line under the action of a resultant force of magnitude $F$ N. The distance between the end-points of the motion is $0.6$ m, and the period of the motion is $0.5$ s. Find the greatest value of $F$ during the motion. [5]
\hfill \mbox{\textit{CAIE FP2 2010 Q1 [5]}}