A block of unknown mass is attached to a spring with a springconstant of 6.00 N/

Question

A block of unknown mass is attached to a spring with a springconstant of 6.00 N/m and undergoessimple harmonic motion with an amplitude of 12.0 cm. When the block is halfway between itsequilibrium position and the end point, its speed is measured to be31.0 cm/s. (a) Calculate the mass of the block.
1 kg
(b) Calculate the period of the motion.
2 s
(c) Calculate the maximum acceleration of the block.
3 m/s2 (a) Calculate the mass of the block.
1 kg
(b) Calculate the period of the motion.
2 s
(c) Calculate the maximum acceleration of the block.
3 m/s2

Explanation / Answer

    Spring constant , K = 6 N/m     Amplitude, A = 12 cm = 0.12 m     Velocity at the midway, V = 31 cm/s =0.31m/s     At the midway, Y = A / 2 = 0.06 m     Velocity, V = ( A 2 -Y 2 )              0.31 = ( 0.12 2 - 0.06 2 )              0.31 = ( 0.0144 - 0.0036 )              0.31 = * 0.1039     Angular frequency, = 2.98 rad/s (a)     Spring constant, K = m 2     Mass, m = K / 2                        = 6 / 2.9 2                 = 0.71 kg (b)     Time-period, T = 2 /                            = 2 / 2.98                            = 2.11 s (c)     Maximum acceleration, a = 2A                                           = 2.98 2 * 0.12          = 1.07 m/s^2

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