A 0.500-kg mass on a spring has velocity as a function of time given by vx(t)=(3.60cms})sin⁡[(4.71rads)t−(π2)]. What are (a) the period; (b) the amplitude; (c) the maximum acceleration of the mass; (d) the force constant of the spring?

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Ben Owens · Accepted Answer

Step 1    Given that the mass of the object is m=0.5kg.    The velocity of the object as a function of time given by    vx(t)=−(3.6cms−1)sin⁡[(4.71rads−1)t−π2]             ​(1)    Since we know that the displacement in SHM is given by    x=Acos⁡[ωt−ϕ]              (2)    By differentiating above equation with respect to time we get the velocity of the object in SHM, so    vx(t)=−Aωsin⁡[ωt−ϕ]            (3)    Now by comparing the equation (1) and (3), we get    Aω=3.6cms−1            (4)    ω=4.7rads−1            (5)    and    ϕ=π2rad             (6)    (a) The period of SHM is given by    P=2πradω    ​=2πrad4.71rads−1    =1.33s            (7)

Matthew Rodriguez · Accepted Answer

Step 2    A=3.6cms−1ω    =3.6cms−14.71rad−1    =0.76cm             (8)

A 0.500-kg mass on a spring has velocity as a

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