A body with a mass of 40 gm is attached to the end of a spring that stretches it

Question

A body with a mass of 40 gm is attached to the end of a spring that stretches it 20 cm. The body is set in motion by displacing the mass by 7 cm downward and then given an initial downward velocity of 5 cm/s. Which of the following is the IVP that describes the motion of the body? (Convert acceleration of gravity to use centimeters.)

Choose correct option from image below.

Section 3.7 Undamped Setup IVP Metric3 A body with a mass of 40 gm is attached to the end of a spring that stretches it 20 cm. The body is set in motion by displacing the mass by 7 cm downward and then given an initial downward velocity of 5 cm/s. Which of the following is the IVP that describes the motion of the body? (Convert acceleration of gravity to use centimeters.) 0 40u" + 19.6u = 0, u(0) = 7, u'(0) = 5 40u"19.6u0, u(O)7, u'(0)-5 u" + 49-0, u(0) = 7, u'(0) = 5 u" + 49u= 0, u(0)--7, u'(0) =-5

Explanation / Answer

Position spring mass system is

m(d^2x/dt^2)+kx =0

Since mass m = 40 gm

we can write function as

40u’’+19.6u =0 ,

Also downward initial position velocity can be written as u(0)= -7 and u’(0) =- 5

Thus option 2 is correct i.e. 40u’’+19.6u =0 , u(0)= -7, u’(0) =- 5

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