Question

plz try to do all these questions Pakka I will mark u brain list I need all questions with step by step answer if one question is wrong then I will report it so try do this only 5question I will give u 15 points

Answer 1

Q1 .   SHM
     Displacement x (t) = A Sin ωt
              velocity v(t)  = A ω Cos ωt
      Acceleration a(t)  = - A ω² Sin ωt

     Given at time t, x(t) = 5m = A Sin ωt   ---(1)
           and  | a(t) | = 20 m/s² =  Aω² Sin ωt   ---(2)
  
     (2) ÷ (1) =>    ω² = 20/5 = 4.    ω = 2 rad/sec.
        f = ω/2π = 1/π rad/sec
        T = 1/f = π sec.
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Q2.   SHM
 
    Displacement from mean position = y(t) = 24 Sin 2πt 
      (General form is y = A Sin ωt )
    Angular frequency = ω = 2π rad/sec
    frequency f = ω/2π = 1 Hz
    time period = 1/f = 1 sec.
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Q3.  SHM
    
    v(t) = 0.007ω Cos ωt   millimetres ,    A = 7 mm given
    Maximum velocity = 4.4 m/s  given.

    So 0.007 ω = 4.4 
    ω = 4.4/0.007 rad/s
    T = 2π/ω = 0.01 sec
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Q4.  SHM
       x = 5 cos(2πt + π/4)  meters
       at t = 1.5 s,   x(t=1.5s) = 5* Cos (3π+π/4) = - 5/√2 meters

         v(t) = - 5 * 2π * Sin (2π t + π/4)  m/sec
       So v(t =1.5 s) = - 5* 2π * sin (3π+π/4) = + 5 π √2  m/s
        
      a(t) = - 5 * (2π)² Cos(2πt + π/4)   m/s²
          a(1.5 s) = + 10 π² √2  m/s²

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Q5.  Simple pendulum.   
        Given that its time period T = 2 second.  (from one side to another it is 1 sec).

        Time period = 2 π √(L/g)
        L = g T² / (4 π²)
           = 9.81 * 2² / (4 π²)
           =  0.994 m   ≈ 1 m

Answer 2

the correct answer is 1 metre