Please help me, thanks a lot. A mass m is attached toa spring of force constant

Question

Please help me, thanks a lot. A mass m is attached toa spring of force constant 74.0 {rm N}/{rm m}and allowed to oscillate. The figure shows a graph of its velocityv_{x} as afunction of time t. At what timesdoes the mass reach the position x=pm A inthe interval between t=0;{rm s}and t=1.8;{rm s}including the endpoints?Find the maximum acceleration of the mass.Find the times at which the maximum acceleration occurs in theinterval between t=0;{rm s}and t=1.8;{rm s}including the endpoints.What is the mass m?

Explanation / Answer

speed is zero at t = 0.4s and 1.2s
-------------------------------------------------------------------------------------------------------------------- Period of the wave is
   T = 1.6s
Angular frequency
   = 2 /T       Speed of the body at any instant is
     V = A cos t
  at t = 1.6 s , V = 20cm/s so
   20 cm /s = A ( 2 / T) cos (2 / T ) t
   20 cm /s = A ( 2 / T) cos (2 / 1.6 ) 1.6
   20 cm /s = A ( 2 / T) cos (2 )     
     20 cm /s = A( 2 / T ) (1)
   A = 20cm /s / ( 2 /T )
   A = 5cm
----------------------------------------------------------------------------------------------------------------- maximum acceleration
   amax= 2 A
   =( 2 / T )2 A
   = ( 2 / 1.6 )2 (5cm )
   =78.53cm/s2  
------------------------------------------------------------------------------------------------------------------- acceleration is maximum when displacement ismaximum
   t = 0.4s and 1.2s
--------------------------------------------------------------------------------------------------------------------        = ( 2 / T ) and = [ k / m ]
   [ k / m ]= ( 2 / T )
   m = kT2 /42   
   =(74)(1.6)2 / 42
      = 4 . 8 kg

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