8) A block of unknown mass is attached to a spring with aspring constant of 5.00

Question

8) A block of unknown mass is attached to a spring with aspring constant of 5.00 N/m and undergoessimple harmonic motion with an amplitude of 11.0 cm. When the block is halfway between itsequilibrium position and the end point, its speed is measured to be28.0 cm/s. (a) Calculate the mass of the block.
________________ kg
(b) Calculate the period of the motion.
_________________ s
(c) Calculate the maximum acceleration of the block.
_________________ m/s2 (a) Calculate the mass of the block.
________________ kg
(b) Calculate the period of the motion.
_________________ s
(c) Calculate the maximum acceleration of the block.
_________________ m/s2

Explanation / Answer

   Amplitude   A   =   11.0   cm                            =   0.11   m    springconstant   k   =   5.00   N/m    Speed at  y   =   A /2,   v0.055   =   28cm/s                                                       =   0.28   m/s    a.   Speed of block atposition   y is given by          vy2   =   2*(A2   -   y2)       Substituting   y   =   A/2          v0.0552   =   2*(A2   -   A2/4)          3 *0.112 * 2 /4   =   0.282       2   =   0.282* 4 / 0.112 * 3             =   12.96       =   12.96          =   3.60      rad/s    also         2   =   k/ m          =>   m   =   k/ 2                         =   5.00/ 12.96                         =   0.356   kg                         =   5.00/ 12.96                         =   0.356   kg       b.   Timeperiod   T   =   2/                                        =   2* 3.14 / 3.60                                        =   1.74   s    c.   maximumaccerleration      =   -2 * A                                                       =   -12.96 * 0.11                                                       =   -1.4256   m/s2    - ve sign indicates that the acceleration isdirected towards the equilibrium position.    - ve sign indicates that the acceleration isdirected towards the equilibrium position.

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