Question

b) A spring mass system is characterized by 1 Nm16 k and kg. 0.1m The system is oscillating with an amplitude of 0.20 m. i) Calculate the angular frequency of oscillation. ii) Obtain an expression for the velocity of the block as a function of displacement and calculate its value at . m1.0x iii) Also calculate energy of the spring-mass system. (

Answer 1

Spring mass system: k = 16 N m⁻¹       m = 0.1 kg
                                  A = amplitude = 0.20 m
1) angular freq  ω
2)  Velocity v = dx/dt  vs  x.
       To find velocity at  x = 0.1 meters.
3)  energy : U+ PE = E

1) ω² = k/m = 16 /0.1 = 160 
     ω = 4√10 rad/sec

3)  Energy:   total:  1/2 k A² = 1/2 * 16 * 0.2² J = 0.32 Joules

2)  displacement  x = A sin ωt
     velocity = v = dx/dt = ω A cos ωt
              v = ω √(A² - x²)

              v = 4 √10 * √(0.2² - 0.1²) = 4 √0.3 m/sec