목차
solm01
solm02
solm03
solm04
solm05
solm06
solm07
solm08
solm09
solm10
solm11
solm12
solm13
solm14
solm15
solm16
solm17
solm18
solm19
solm20
solm21
solm22
solm02
solm03
solm04
solm05
solm06
solm07
solm08
solm09
solm10
solm11
solm12
solm13
solm14
solm15
solm16
solm17
solm18
solm19
solm20
solm21
solm22
본문내용
1.1 You are given the following differential equation with the initial condition, v(t = 0) = 0,
2vmcgdtdvd−=
Multiply both sides by m/cd
2vgcmdtdvcmdd−=
Define dcmga/=
22vadtdvcmd−=
Integrate by separation of variables,
dtmcvadvd∫∫=−22
A table of integrals can be consulted to find that
axaxadx122tanh1−=−∫
Therefore, the integration yields
Ctmcavad+=−1tanh1
If v = 0 at t = 0, then because tanh–1(0) = 0, the constant of integration C = 0 and the solution is
tmcavad=−1tanh1
This result can then be rearranged to yield
⎟⎟⎠⎞⎜⎜⎝⎛=tmgccgmvddtanh
1.2 This is a transient computation. For the period from ending June 1:
PROPRIETARY MATERIAL. © The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual
Balance = Previous Balance + Deposits – Withdrawals
may be displayed, reproduced or distributed in any form or by any means, without the prior written permission of the
publisher, or used beyond the limited distribution to teachers and educators permitted by McGraw-Hill
2vmcgdtdvd−=
Multiply both sides by m/cd
2vgcmdtdvcmdd−=
Define dcmga/=
22vadtdvcmd−=
Integrate by separation of variables,
dtmcvadvd∫∫=−22
A table of integrals can be consulted to find that
axaxadx122tanh1−=−∫
Therefore, the integration yields
Ctmcavad+=−1tanh1
If v = 0 at t = 0, then because tanh–1(0) = 0, the constant of integration C = 0 and the solution is
tmcavad=−1tanh1
This result can then be rearranged to yield
⎟⎟⎠⎞⎜⎜⎝⎛=tmgccgmvddtanh
1.2 This is a transient computation. For the period from ending June 1:
PROPRIETARY MATERIAL. © The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual
Balance = Previous Balance + Deposits – Withdrawals
may be displayed, reproduced or distributed in any form or by any means, without the prior written permission of the
publisher, or used beyond the limited distribution to teachers and educators permitted by McGraw-Hill
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