114 學年度臺灣大學轉學生招生考試｜第 58 題
普通物理學(A)
- Tnew = 0.5 T0
- Tnew = T0
- Tnew = √2 T0
- Tnew = 2 T0
- Tnew = 3 T0
提示
The drop happens at maximum extension, where the oscillator's speed is momentarily zero. Think about what is conserved when the added block sticks, and how the period depends on the total mass.
正確答案
正解：C
詳解
A. (A) T_new = 0.5 T₀ — incorrect. Adding mass increases the period, not decreases it; period grows with √m.
B. (B) T_new = T₀ — incorrect. The total oscillating mass changes, so the period cannot stay the same.
C. (C) T_new = √2 T₀ — correct. At maximum extension the speed is zero, so the perfectly inelastic landing loses no kinetic energy and the spring constant is unchanged. The mass doubles (m → 2m). Since T = 2π√(m/k), T_new = 2π√(2m/k) = √2 · T₀.
D. (D) T_new = 2 T₀ — incorrect. This would require the mass to quadruple; it only doubles, so the factor is √2, not 2.
E. (E) T_new = 3 T₀ — incorrect. There is no factor of 3; the period scales with the square root of the mass ratio.
