Practice free Oscillations (Physics) NEET multiple-choice questions online with instant answers and detailed explanations. No login required.
A particle oscillating under the influence of a force F(t) = -kx(t) is called a:
The context states: 'Note that the force in Eq. (13.13) is linearly proportional to x(t). A particle oscillating under such a force is, therefore, calling a linear harmonic oscillator.' (NCERT, page 267)
If the force acting on an oscillating particle contains additional terms proportional to x², x³, etc., the oscillator would be classified as a:
The text explains: 'In the real world, the force may contain small additional terms proportional to x², x³, etc. These then are called non-linear oscillators.' (NCERT, page 267)
Simple Harmonic Motion can be defined in two equivalent ways. One by the displacement equation x(t) = A cos(ωt + φ). What is the other equivalent way?
The context states: 'To summarise the discussion so far, simple harmonic motion can be defined in two equivalent ways, either by Eq. (13.4) for displacement or by Eq. (13.13) that gives its force law.' Eq. (13.13) is F(t) = -kx(t). (NCERT, page 267)
To derive the displacement equation x(t) from the force law F(t) = -kx(t), one needs to perform:
The context mentions: 'Going from Eq. (13.4) to Eq. (13.13) required us to differentiate two times. Likewise, by integrating the force law Eq. (13.13) two times, we can get back Eq. (13.4).' (NCERT, page 267)
For a spring-mass system executing SHM, if the mass 'm' is increased while the spring constant 'k' remains the same, the angular frequency ω will:
From the formula ω = √(k/m), given in the text (Eq. 13.14b), if 'm' increases and 'k' remains constant, ω will decrease. (NCERT, page 267)
A body of mass 'm' is attached to two identical springs of spring constant 'k' each, connected in parallel with the mass between fixed supports. If the mass is displaced, the net restoring force F will be:
In Example 13.6, when two identical springs (spring constant k) are attached to a mass 'm' with fixed supports such that one spring elongates and the other compresses by 'x', the forces are Fâ‚ = -kx and Fâ‚‚ = -kx. The net force F = Fâ‚ + Fâ‚‚ = -2kx. (NCERT, page 268)
What is the period of oscillation for a mass 'm' attached to two identical springs of spring constant 'k' each, connected as described in Example 13.6?
In Example 13.6, the net restoring force is F = -2kx. Comparing this with F = -K_eff x, we find the effective spring constant K_eff = 2k. The period of oscillation T = 2π√(m/K_eff). Substituting K_eff = 2k gives T = 2π√(m/2k). (NCERT, page 268)
The total mechanical energy of a harmonic oscillator is given by E = ½kA². This energy:
The context states: 'The total mechanical energy of a harmonic oscillator is thus independent of time as expected for motion under any conservative force.' (NCERT, page 269)
In SHM, at which state is the potential energy maximum and kinetic energy zero?
The text clarifies: 'For x = 0, the energy is kinetic; at the extremes x = ± A, it is all potential energy.' At extreme positions, the velocity is zero, hence kinetic energy is zero, and the potential energy is maximum. (NCERT, page 269)
What is the relationship between angular frequency (ω), spring constant (k), and mass (m) for a particle in SHM?
The text clearly states the relationship as ω = k/m (13.14b). This is a crucial formula for SHM. (NCERT, page 267)
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