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6 public questions tagged with this topic.

Spring-Mass System and Combination of Springs

Two identical springs (\( k = 75 \, \text{N/m} \)) are attached to a \( 1.5 \, \text{kg} \) mass as in Fig. 13.14. What

**Oscillation of mass attached to spring** follows Hooke's law F = -k x, SHM with ω = √(k/m). Effective stiffness for two identical springs in parallel doubles, k_eff = 2k, increasing frequency by √2, while series halves stiffness to k/2, lowering frequency. Energy E = ½ k_eff A². Effective kₑff = 2k = 2 × 75 = 150 N/m . ω = √((kₑff/m)) = √((150/1.5)) = √(100) = 10 rad/s . v = (ω/2π) = (10/2 × 3.14) ≈ 1.59 Hz . Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result

Ref: NCERT > Physics Book > Oscillations > Spring-Mass System and Combination of Springs

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Spring-Mass System and Combination of Springs

Two identical springs (\( k = 100 \, \text{N/m} \)) are attached to a \( 1 \, \text{kg} \) mass as in Fig. 13.14. What i

**Mass-spring dynamics** show T depends on mass and stiffness, independent of amplitude for ideal spring. Given T and m, k = 4π² m/T² extracted, and energy E = ½ k A² connects amplitude to total mechanical energy, illustrating isochronism. Net force: F = -2kx , so effective kₑff = 2k = 200 N/m . T = 2π √((m/kₑff)) = 2π √((1/200)) ≈ 0.44 s . Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result 0.44 s follows, reflecting SHM dependence on amplitude A, ω and system parameters.

Ref: NCERT > Physics Book > Oscillations > Spring-Mass System and Combination of Springs

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Spring-Mass System and Combination of Springs

Two identical springs (\( k = 60 \, \text{N/m} \)) are attached to a \( 1.2 \, \text{kg} \) mass as in Fig. 13.14. What

**Mass-spring dynamics** show T depends on mass and stiffness, independent of amplitude for ideal spring. Given T and m, k = 4π² m/T² extracted, and energy E = ½ k A² connects amplitude to total mechanical energy, illustrating isochronism. Effective kₑff = 2k = 2 × 60 = 120 N/m . ω = √((kₑff/m)) = √((120/1.2)) = √(100) = 10 rad/s . v = (ω/2π) = (10/2 × 3.14) ≈ 1.59 Hz . Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result 1.59 Hz follows, reflecting SHM dependence on amplitude A, ω and system parameters.

Ref: NCERT > Physics Book > Oscillations > Spring-Mass System and Combination of Springs

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Spring-Mass System and Combination of Springs

Two identical springs (\( k = 70 \, \text{N/m} \)) are attached to a \( 1.4 \, \text{kg} \) mass as in Fig. 13.14. What

**Oscillation of mass attached to spring** follows Hooke's law F = -k x, SHM with ω = √(k/m). Effective stiffness for two identical springs in parallel doubles, k_eff = 2k, increasing frequency by √2, while series halves stiffness to k/2, lowering frequency. Energy E = ½ k_eff A². Effective kₑff = 2k = 2 × 70 = 140 N/m . ω = √((kₑff/m)) = √((140/1.4)) = √(100) = 10 rad/s . v = (ω/2π) = (10/2 × 3.14) ≈ 1.59 Hz . Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result

Ref: NCERT > Physics Book > Oscillations > Spring-Mass System and Combination of Springs

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