Physics · Oscillations · NEET
KE and PE change with position, but they change in opposite ways. When the body moves toward the mean position, PE falls and KE rises by the exact same amount. When it moves toward the extreme, KE falls and PE rises by the same amount. So at every instant KE + PE = 1/2 k A^2, a fixed number. Energy is only being transferred between two forms, not created or lost (assuming no friction).
No. This is the key idea. At any position x: KE = 1/2 k (A^2 - x^2) and PE = 1/2 k x^2. Add them: KE + PE = 1/2 k A^2 - 1/2 k x^2 + 1/2 k x^2 = 1/2 k A^2. The x^2 terms cancel, so total energy has no x in it. It is the same at the mean position, at the extreme, and everywhere in between.
It depends on three things: mass m, angular frequency omega, and amplitude A. The formula is E = 1/2 m omega^2 A^2 = 1/2 k A^2 (since k = m omega^2). Notice E is proportional to A^2 (square of amplitude) and to omega^2. If you double the amplitude, the total energy becomes 4 times larger. It does NOT depend on the position or the time.
At the mean position all the energy is kinetic. Since PE = 1/2 k x^2 and x = 0 there, PE = 0 and KE is maximum, equal to the full total energy 1/2 k A^2. This is why the body moves fastest at the mean position. Nothing is lost - the PE simply turned fully into KE.
It is not a maximum at any point - it is the SAME everywhere. Students confuse this because KE is maximum at the mean position and PE is maximum at the extremes. But the SUM (total energy) is a flat horizontal line if you plot it against position or time. Only the individual KE and PE curves rise and fall.
The sum of the kinetic energy and potential energy of a simple pendulum bob is 0.02 J. The speed of the bob at its equilibrium position is approximately (mass of the bob = 20 g)
Try the real previous-year questions from this chapter — each with the answer and a full solution.
E = 1/2 m omega^2 A^2, which is also written as E = 1/2 k A^2 because the spring constant k = m omega^2. Here m is mass, omega is angular frequency, A is amplitude, and k is force constant.
Yes, in ideal SHM (no friction or damping) the total mechanical energy is constant at every instant and every position. KE and PE keep exchanging, but their sum is fixed at 1/2 k A^2.
Total energy is proportional to the square of the amplitude (E is proportional to A^2). If amplitude doubles, energy becomes 4 times; if amplitude triples, energy becomes 9 times.
It has no single maximum point - it is the same everywhere. Only KE (max at mean) and PE (max at extremes) change; the total stays the same constant value.
Because KE = 1/2 k(A^2 - x^2) and PE = 1/2 k x^2. When added, the x^2 terms cancel, leaving E = 1/2 k A^2, which contains no x. So position does not affect the total.
It does not vary at all - its frequency of variation is zero. Only the individual KE and PE vary, and they vary at double the frequency of the motion (2n), while their sum stays flat.
